PROGRAM & ABSTRACTS - Universidad de Zaragozametodosestadisticos.unizar.es/~jaca2011/Program.pdf · PROGRAM & ABSTRACTS. ... Sara de la Rosa de S aa, ... Analysis of Demographic and

THE PYRENEES

INTERNATIONAL WORKSHOP

AND SUMMER SCHOOL

ON STATISTICS, PROBABILITY AND

OPERATIONS RESEARCH

Jaca (Huesca), Spain, 13-16 September, 2011

PROGRAM & ABSTRACTS

The Pyrenees InternationalWorkshop and SummerSchool on Statistics,

Probability and OperationsResearch

PROGRAM & ABSTRACTS

SPO 2011

Jaca (Huesca), Spain, September 13-16, 2011

Contents

COMMITTEES 9

PROGRAM 13

General Schedule 15

Tuesday September 13 17

Wednesday September 14 19

Thursday September 15 21

Friday September 16 23

ABSTRACTS 25

Courses and Conferences 27

Precedence-type testing and applications 29N. Balakrishnan

Design of experiments for nonlinear models 30J. Lopez Fidalgo

Random fuzzy sets: a probabilistic tool to develop statistics with im-precise data 31

M.A. Gil

Multi-class data exploration using space transformed visualization plots 32Rida E. Moustafa, Ali S. Hadi and Jurgen Symanzik

Contributed Sessions 33

Modelling a bivariate counting process. An application to the occur-rence of extreme heat events 35

Jesus Abaurrea, Jesus Asın and Ana C. Cebrian

Development of a daily to hourly rainfall disaggregation model 36J. Abaurrea, J. Asın, A.C. Cebrian and N. Gavın

On the convergence rates of multivariate higher-order polynomial ker-nels 37

B. A. Afere and F. O. Oyegue

A heuristic for identifying unknown agents in a transaction network 38David Alcaide, Joaquın Sicilia and Miguel Angel Gonzalez Sierra

SPO 2011 Jaca, September 13–16th 2011 CONTENTS

Labour accessibility and residence attractiveness: a Bayesian analysisbased on Spatial nteraction models 39

Marıa Pilar Alonso, Asuncion Beamonte, Pilar Gargallo and Manuel Salvador

Infinite time horizon crew scheduling modeling for a train transporta-tion problem 40

Jorge Amaya,Hector Ramırez and Paula Uribe

Optimal Experimental Designs for Time Series Models 41Mariano Amo-Salas and Jesus Lopez-Fidalgo

On spectral and statistical analysis of heavy-tailed Kolmogorov Pearsondiffusions 42

Florin Avram, Nikolai Leonenko and Nenad Suvak

Robustness and Density Power Divergence Measures 43Ayanendranath Basu, Abhijit Mandal, Nirian Martin and Leandro Pardo

Asymptotic normality through factorial cumulants and partitions iden-tities 44

Konstancja Bobecka, Pawe l Hitczenko, Fernando Lopez-Blazquez, GrzegorzRempa la and Jacek Weso lowski

Semiparametric estimation of a two-components mixture of regressionmodels 45

Laurent Bordes, Ivan Kojadinovic and Pierre Vandekerkhove

Extending the Classical Koziol-Green model by using a copula function 46Roel Braekers and Auguste Gaddah

Classification trees for the characterization of some aragonaise grapevinevarieties 47

Jose Casanova, Beatriz Lacruz and Jesus M. Ortiz

Two perspectives of design and modeling when some independent vari-able is uncontrollable. 48

Vıctor Casero-Alonso and Jesus Lopez-Fidalgo

Free Completely Random Measures 49Francesca Collet, Fabrizio Leisen and Antonio Lijoi

Nonparametric predictive pairwise comparison with competing risks 50Tahani Coolen-Maturi

A Comparative Study of Bullwhip Effect in a Multi-Echelon Forward-Reverse Supply Chain 51

Debabrata Das and Pankaj Dutta

4

CONTENTS SPO 2011 Jaca, September 13–16th 2011

Likert and fuzzy scales: an empirical comparison through the MSE 52Sara de la Rosa de Saa, Marıa Teresa Lopez and Marıa Asuncion Lubiano

Statistical inference based on restricted sequential order statistics forweibull distribution with a power trend model 53

M. Doostparast and E. Velayati Moghaddam

A proposed Markov model for predicting the structure of a multi-echelon educational system in Nigeria 54

Virtue U. Ekhosueh and Augustine A. Osagiede

Analysis of Demographic and Health Survey Data of Turkey with BayesianNetworks and Association Analysis 55

Derya Ersel and Suleyman Gunay

Linear combination of biomarkers to improve diagnostic accuracy inProstate cancer 56

Luis Mariano Esteban, Gerardo Sanz and Angel Borque

Optimum Designs for Enzyme Inhibition Models: Algorithmic Ap-proach 57

Mercedes Fernandez-Guerrero, Raul Martın-Martın and Licesio J. Rodrıguez-Aragon

An study of some frailty models 58J.M. Fernandez-Ponce, F. Palacios-Rodrıguez and R. Rodrıguez-Grinolo

Response-adaptive designs based on the Ehrenfest urn 59Arkaitz Galbete, Jose Antonio Moler and Fernando Plo

Maximum likelihood and bayesian estimates and prediction for geomet-ric distribution based on δ-records 60

R. Gouet, F.J. Lopez, L.P. Maldonado and G. Sanz

Geometric Records 61Raul Gouet, F. Javier Lopez and Gerardo Sanz

On the structure of near-record values 62Raul Gouet, F. Javier Lopez and Gerardo Sanz

A least squares estimation method for high heteroscedastic linear mod-els 63

Ali S. Hadi, Beatriz Lacruz and Ana Perez-Palomares

A Bootstrap Modification of the Multivariate Boosting Algorithm inKDE 64

Cyril Chukwuka Ishiekwene

5

SPO 2011 Jaca, September 13–16th 2011 CONTENTS

Simulating random variables with Lindley or Poisson–Lindley distribu-tion 65

Pedro Jodra

The Speed of Random Walks on Trees and Electric Networks 66

Mokhtar Konsowa and Fahimah Al-Awadhi

Family of estimators of population variance in succesive sampling 67

Nursel Koyuncu

To obtain the number of Hidden Nodes in ELM methodology 68

Beatriz Lacruz, David Lahoz and Pedro M. Mateo

CID sequences and Bayesian non parametrics 69

Fabrizio Leisen

The number of records in geometric samples 70

Fernando Lopez-Blazquez and Begona Salamanca-Mino

Logic regression model versus classical linear and logistic regressionmodels 71

Magdalena Malina

Phi-divergence test statistics for loglinear models subject to constraintsof likelihood ratio order 72

Nirian Martin, Raquel Mata and Leandro Pardo

The problem of random generation of non-additive measures 73

P. Miranda, E. F. Combarro and I. Dıaz

Some contributions to the class of controlled two-sex branching pro-cesses 74

Manuel Molina, Manuel Mota and Alfonso Ramos

The powers of the stochastic Gompertz diffusion process: Statisticalinference 75

A. Nafidi, R. Gutierrez, R. Gutierrez-Sanchez and E. Ramos

A Bayesian Model for Longitudinal Circular Data 76

Gabriel Nunez Antonio and Eduardo Gutierrez Pena

A decision model for a newsvendor inventory problem with an extror-dinary order 77

Valentın Pando, Luis A. San-Jose, Juan Garcıa-Laguna and Joaquın Sicilia

6

CONTENTS SPO 2011 Jaca, September 13–16th 2011

Landmark Prediction of Long Term Survival Incorporating Short TermEvent Time Information 78

Layla Parast, Su-Chun Cheng and Tianxi Cai

About some old and new non-parametric control charts 79Christian Paroissin and Jean-Christophe Turlot

Design of optimal progressively censored sampling plans using averagerisks 80

Carlos J. Perez-Gonzalez and Arturo J. Fernandez

Modeling Operational Risk with Bayesian extreme value theory 81Maria Elena Rivera Mancia

Study of A-optimality for the univariate logistic model with randomeffects 82

M.T. Santos Martın, J. M. Rodrıguez Dıaz and C. Tommasi

Comparing two approaches to the median of a random interval 83Beatriz Sinova, Ana Colubi and Gerardo Sanz

Exit and ruin times for general renewal risk-models 84Javier Villarroel

Ageing properties of some bivariate distributions from the Farlie-Gumbel-Morgenstern family 85

Juana-Marıa Vivo and Manuel Franco

Song’s measure of the shape and its application to detect departurefrom a specific elliptic distribution 86

Konstantinos Zografos and Apostolos Batsidis

A Bayesian approach to bandwidth selection in univariate associatekernel estimation 87

N. Zougab, S. Adjabi and C.C. Kokonendji

INDEX OF AUTHORS 89

LIST OF PARTICIPANTS 93

7

COMMITTEES

COMMITTEES SPO 2011 Jaca, September 13–16th 2011

SCIENTIFIC COMMITTEE

Laurent Bordes (Universite de Pau et des Pays de l’Adour, France).

Wenceslao Gonzalez Manteiga (Universidad de Santiago de Compostela, Spain).

Raul Gouet (Universidad de Chile, Chile).

Fermın Mallor (Universidad Publica de Navarra, Spain).

Servet Martınez (Universidad de Chile, Chile).

Jose Antonio Moler (Universidad Publica de Navarra, Spain).

Domingo Morales (Universidad Miguel Hernandez, Spain).

Evsey Morozov (University of Petrozavodsk, Russia).

Leandro Pardo (Universidad Complutense de Madrid, Spain).

Christian Paroissin (Universite de Pau et des Pays de l’Adour, France).

Justo Puerto (Universidad de Sevilla, Spain).

Gerardo Sanz (Universidad de Zaragoza, Spain).

Joaquın Sicilia (Universidad de La Laguna, Spain).

ORGANIZING COMMITTEE

Isolina Alberto (Universidad de Zaragoza, Spain).

Marıa Asuncion Beamonte (Universidad de Zaragoza, Spain).

Ana Carmen Cebrian (Universidad de Zaragoza, Spain).

Luis Mariano Esteban (Universidad de Zaragoza, Spain).

Beatriz Lacruz (Universidad de Zaragoza, Spain).

David Lahoz (Universidad de Zaragoza, Spain).

Javier Lopez (Universidad de Zaragoza, Spain).

Pedro Mateo (Universidad de Zaragoza, Spain).

Ana Perez-Palomares (Universidad de Zaragoza, Spain).

Gerardo Sanz (Universidad de Zaragoza, Spain).

11

PROGRAM

GENERAL SCHEDULE SPO 2011 Jaca, September 13–16th 2011

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TUESDAY SEPTEMBER 13 SPO 2011 Jaca, September 13–16th 2011

Tuesday September 13

8:30-9:30 Registration

9:30-10:00 Welcome

10:00-11:00 Course I

Precedence-type testing and applications

N. Balakrishnan

11:00-11:30 Coffee break

11:30-12:30 Course II

Design of experiments for nonlinear models

Jesus Lopez-Fidalgo

12:30 Contributed Session I. Chairman: Konstantinos Zografos

12:30-12:50 Song’s measure of the shape and its application to detect departurefrom a specific elliptic distribution

Konstantinos Zografos and Apostolos Batsidis

12:50-13:10 Ageing properties of some bivariate distributions from the Farlie-Gumbel-Morgenstern family

Manuel Franco and Juana-Marıa Vivo

13:10-13:30 Extending the Classical Koziol-Green model by using a copula function

Roel Braekers and Auguste Gaddah

13:30-13:50 Optimal Experimental Designs for Time Series Models

Mariano Amo-Salas and Jesus Lopez-Fidalgo

13:50-16:00 Lunch Time

16:00 Contributed Session II. Chairman: Manuel Molina

16:00-16:20 Some contributions to the class of controlled two-sex branching pro-cesses

Manuel Molina, Manuel Mota and Alfonso Ramos

17

SPO 2011 Jaca, September 13–16th 2011 TUESDAY SEPTEMBER 13

16:20-16:40 Free Completely Random Measures

Francesca Collet, Fabrizio Leisen and Antonio Lijoi

16:40-17:00 Modelling a bivariate counting process. An application to the occur-rence of extreme heat events

Jesus Abaurrea, Jesus Asın and Ana C. Cebrian

17:00-17:20 The Speed of Random Walks on Trees and Electric Networks

Mokhtar Konsowa and Fahimah Al-Awadhi

17:20-18:00 Coffee Break

18:00 Contributed Session III. Chairman: Licesio J. Rodrıguez-Aragon

18:00-18:20 Optimum Designs for Enzyme Inhibition Models: Algorithmic Ap-proach

Mercedes Fernandez-Guerrero, Raul Martın-Martın and Licesio J. Rodrıguez-Aragon

18:20-18:40 Nonparametric predictive pairwise comparison with competing risks

Tahani Coolen-Maturi

18:40-19:00 Landmark Prediction of Long Term Survival Incorporating Short TermEvent Time Information

Layla Parast, Su-Chun Cheng and Tianxi Cai

19:00-19:20 Comparing two approaches to the median of a random interval

Beatriz Sinova, Ana Colubi and Gerardo Sanz

19:20-19:40 Logic regression model versus classical linear and logistic regressionmodels

Magdalena Malina

20:00 Opening Ceremony – Spanish wine

18

WEDNESDAY SEPTEMBER 14 SPO 2011 Jaca, September 13–16th 2011

Wednesday September 14

9:00-10:00 Course II


Jesus Lopez Fidalgo

10:00-11:00 Course I


N. Balakrishnan


11:30-12:30 Conference

Random fuzzy sets: a probabilistic tool to develop statistics with imprecise data

Marıa Angeles Gil

12:30 Contributed Session IV. Chairman: Laurent Bordes

12:30-12:50 Semiparametric estimation of a two-components mixture of regressionmodels

Laurent Bordes, Ivan Kojadinovic and Pierre Vandekerkhove

12:50-13:10 Robustness and Density Power Divergence Measures

Ayanendranath Basu, Abhijit Mandal, Nirian Martin and Leandro Pardo

13:10-13:30 Two perspectives of design and modeling when some independent vari-able is uncontrollable

Vıctor Casero-Alonso and Jesus Lopez-Fidalgo

13:10-13:30 On the structure of near-record values

Raul gouet, F. Javier Lopez and Gerardo Sanz


16:00 Contributed Session V. Chairman: Pedro Miranda

16:00-16:20 The problem of random generation of non-additive measures

P. Miranda, E. F. Combarro and I. Dıaz

19

SPO 2011 Jaca, September 13–16th 2011 WEDNESDAY SEPTEMBER 14

16:20-16:40 A proposed Markov model for predicting the structure of a multi-echelon educational system in Nigeria

Virtue U. Ekhosueh and Augustine A. Osagiede

16:40-17:00 A Comparative Study of Bullwhip Effect in a Multi-Echelon Forward-Reverse Supply Chain

Debabrata Das and Pankaj Dutta

17:00-17:20 Infinite time horizon crew scheduling modeling for a train transporta-tion problem

Jorge Amaya,Hector Ramırez and Paula Uribe

17:20-17:40 A Bootstrap Modification of the Multivariate Boosting Algorithm inKDE

Cyril Chukwuka Ishiekwene

18:00 Guided visit to Jaca

20

THURSDAY SEPTEMBER 15 SPO 2011 Jaca, September 13–16th 2011

Thursday September 15

9:00-10:00 Course I


N. Balakrishnan

10:00-11:00 Course II


Jesus Lopez Fidalgo


11:30-12:30 Poster Session. Chairman: David Lahoz

1. Simulating random variables with Lindley or Poisson–Lindley distribution

Pedro Jodra

2. The powers of the stochastic Gompertz diffusion process: Statistical infer-ence

A. Nafidi, R. Gutierrez, R. Gutierrez-Sanchez and E. Ramos

3. Modeling Operational Risk with Bayesian extreme value theory

Maria Elena Rivera Mancia

4. Study of A-optimality for the univariate logistic model with random effects

M.T. Santos Martın, J. M. Rodrıguez Dıaz and C. Tommasi

5. Linear combination of biomarkers to improve diagnostic accuracy in Prostatecancer

Luis Mariano Esteban, Gerardo Sanz and Angel Borque

6. An study of some frailty models

J.M. Fernandez-Ponce, F. Palacios-Rodrıguez and R. Rodrıguez-Grinolo

7. Phi-divergence test statistics for loglinear models subject to constraints oflikelihood ratio order

Nirian Martin, Raquel Mata and Leandro Pardo

8. A decision model for a newsvendor inventory problem with an extrordinaryorder

Valentın Pando, Luis A. San-Jose, Juan Garcıa-Laguna and Joaquın Si-cilia

9. Design of optimal progressively censored sampling plans using average risks

Carlos J. Perez-Gonzalez and Arturo J. Fernandez

21

SPO 2011 Jaca, September 13–16th 2011 THURSDAY SEPTEMBER 15

10. Development of a daily to hourly rainfall disaggregation model

J. Abaurrea, J. Asın, A.C. Cebrian and N. Gavın

11. Classification trees for the characterization of some aragonaise grapevinevarieties

Jose Casanova, Beatriz Lacruz and Jesus M. Ortiz

12. To obtain the number of Hidden Nodes in ELM methodology

Beatriz Lacruz, David Lahoz and Pedro M. Mateo

13. A heuristic for identifying unknown agents in a transaction network

David Alcaide, Joaquın Sicilia and Miguel Angel Gonzalez Sierra

14. A Bayesian Model for Longitudinal Circular Data

Gabriel Nunez Antonio, Eduardo Gutierrez Pena

15. A least squares estimation method for high heteroscedastic linear models

Ali S. Hadi, Beatriz Lacruz and Ana Perez-Palomares

16. A Bayesian approach to bandwidth selection in univariate associate kernelestimation

N. Zougab, S. Adjabi and C.C. Kokonendji

12:30 Contributed Session VI. Chairman: Raul Gouet

12:30-12:50 Geometric Records

Raul Gouet, F. Javier Lopez and Gerardo Sanz

12:50-13:10 The number of records in geometric samples

Fernando Lopez-Blazquez and Begona Salamanca-Mino

13:10-13:30 Asymptotic normality through factorial cumulants and partitions iden-tities

Konstancja Bobecka, Pawe l Hitczenko, Fernando Lopez-Blazquez, Grzegorz Rempa laand Jacek Weso lowski

13:30-13:50 Exit and ruin times for general renewal risk-models

Javier Villarroel


16:00 Excursion

22

FRIDAY SEPTEMBER 16 SPO 2011 Jaca, September 13–16th 2011

Friday September 16

9:00-10:00 Course II

Discussion session: Design of experiments for nonlinear models

Jesus Lopez Fidalgo

10:00-11:00 Course I

Discussion session: Precedence-type testing and applications

N. Balakrishnan


11:30-12:30 Conference

Multi-class data exploration using space transformed visualization plots

Rida E. Moustafa, Ali S. Hadi and Jurgen Symanzik

12:30 Contributed Session VII. Chairman: Christian Paroissin

12:30-12:50 Statistical inference based on restricted sequential order statistics forweibull distribution with a power trend model

M. Doostparast and E. Velayati Moghaddam

12:50-13:10 Family of estimators of population variance in succesive sampling

Nursel Koyuncu

13:10-13:30 About some old and new non-parametric control charts

Christian Paroissin and Jean-Christophe Turlot

13:30-13:50 Maximum likelihood and bayesian estimates and prediction for geomet-ric distribution based on δ-records

R. Gouet, F.J. Lopez, L.P. Maldonado and G. Sanz


16:00 Contributed Session VIII. Chairman: M. Salvador

16:00-16:20 On the convergence rates of multivariate higher-order polynomial ker-nels

B. A. Afere and F. O. Oyegue

23

SPO 2011 Jaca, September 13–16th 2011 FRIDAY SEPTEMBER 16

16:20-16:40 Analysis of Demographic and Health Survey Data of Turkey with BayesianNetworks and Association Analysis

Derya Ersel and Suleyman Gunay

16:40-17:00 Likert and fuzzy scales: an empirical comparison through the MSE

Sara de la Rosa de Saa, Marıa Teresa Lopez and Marıa Asuncion Lubiano

17:00-17:20 Labour accessibility and residence attractiveness: a Bayesian analysisbased on Spatial nteraction models

Marıa Pilar Alonso, Asuncion Beamonte, Pilar Gargallo and Manuel Salvador


18:00 Contributed Session VIII. Chairman: Fabrizio Leisen

18:00-18:20 CID sequences and Bayesian non parametrics

Fabrizio Leisen

18:20-18:40 Response-adaptive designs based on the Ehrenfest urn

Arkaitz Galbete, Jose Antonio Moler and Fernando Plo

18:40-19:00 On spectral and statistical analysis of heavy-tailed Kolmogorov Pearsondiffusions

Florin Avram, Nikolai Leonenko and Nenad Suvak

21:00 Closing Dinner

24

ABSTRACTS

COURSES

AND

INVITED

CONFERENCES

COURSES AND CONFERENCES SPO 2011 Jaca, September 13–16th 2011


N. Balakrishnan1,

SUMMARY

In this course, I will first start with an introduction to the concept of precedencetesting and explain its features including the derivation of the exact null distributionand its power function against Lehmann alternatives. I will show that this test,though simple and quite effective, suffers from a ”masking effect” and to avoid thisproblem, I will propose maximal precedence test and weighted precedence test. Iwill then introduce Wilcoxon-type precedence tests and discuss their null and powerproperties for a wide class of alternatives.

As the next stage, I will discuss the adaptation of precedence tests when theavailable samples are progressively censored. I will explain how precedence tests canbe developed based on Kaplan-Meier estimates and evaluate their power performance.

Finally, if time permits, I shall explain the precedence testing in the case of mul-tiple samples as well as their use in the selection of best treatments when multipletreatments are compared.

Through out the presentation, I will present several computational results as wellas illustrative examples.

Keywords: Precedence testing, power function, progressive censoring

AMS Classification: 62N03, 62N01

References

[1] Balakrishnan, N. and Tony Ng, H. K. (2006). Precedence-type tests andapplications. Wiley, Hoboken, New Jersey.

1Department of Mathematics and StatisticsMcMaster UniversityHamilton, Ontario. [email protected]

29

SPO 2011 Jaca, September 13–16th 2011 COURSES AND CONFERENCES


Jesus Lopez-Fidalgo1

SUMMARY

This course will try to show why experimental design is an exciting area in statistics.You may have had the chance to work in problems related to many different fields,from different statistical methodologies to any experimental science. Wherever thereis a variable under the control of the experimenter there is an opportunity to look foran experimental design in order to optimize the results. The course will be focused onoptimal experimental design more than in the classical experimental design approach.The theory applies in an elegant and rigorous way to linear models, but nonlinearmodels frequently show up in practice. After stressing the importance of designing anexperiment a brief introduction to the theory for linear models will be made. Thenthere will be time to adjust this theory to nonlinear models. Some interesting booksto be initiated in this area are [2], [4], [5], [3] or the most recent [1].

Keywords: Exact and approximate design, Fisher information matrix, optimalitycriteria, general equivalence theorem

AMS Classification: 62K05

References

[1] Atkinson A. C., Doney A. N. and Tobias R. (2007). Optimum ExperimentalDesigns, With SAS. Oxford science publications, Oxford.

[2] Fedorov V. (1972). Theory of optimal experiments. Academic press, New York.

[3] Fedorov V. and Hackl P. (1997). Model-oriented design of experiments.Springer, New York.

[4] Pazman A. (1986). Foundations of Optimum Experimental Design. D. ReidelPub., New York.

[5] Pukelsheim F. (1993). Optimal Design of Experiments. John Wiley & Sons, NewYork.

1University of Castilla-La [email protected]

30

COURSES AND CONFERENCES SPO 2011 Jaca, September 13–16th 2011

Random fuzzy sets: a probabilistic toolto develop statistics with imprecise data∗

Marıa Angeles Gil

SUMMARY

Random fuzzy sets (for short RFSs) are random elements taking on values on classesof fuzzy sets of Euclidean spaces. They have been introduced as a mathematical modelfor random mechanisms generating imprecise values which can be properly formalizedby means of fuzzy sets.

The model involves a certain Borel-measurability assumption guaranteeing one canrigourously refer to: the induced distribution of an RFS, the stochastic independenceof RFSs, a simple random sample from an RFS, and so on.

In spite of the fact that RFSs can be viewed as a non-trivial special type offunctional-valued random elements, some specific features (mostly related to the arith-metic between fuzzy values) state crucial differences between them. Thus, on the basisof an isometrical embedding, fuzzy values can be identified with functional ones, al-though through such an identification the classes of fuzzy values are associated withclosed convex cones of Hilbert spaces but not Hilbertian themselves.

In analyzing fuzzy data for statistical purposes several ideas and approaches fromthe analysis of real/vectorial data can be extended, but often special care should betaken in avoiding the inconveniences due to the lack of: linearity and complete or-dering in handling fuzzy data; friendly and realistic models for the distributions ofRFSs; Central Limit Theorems for RFSs where the limit distribution corresponds toa random element taking on values inside the associated cone. These inconveniencesare ‘bypassed’ by considering a distance-based methodology using a generalized boos-trapped Central Limit Theorem.

Keywords: fuzzy arithmetic, metrics between fuzzy values, random fuzzy sets.

AMS Classification: 62A86

Departamento de Estadıstica e I.O. y D.M.,Universidad de Oviedo, 33071 Oviedo, [email protected]

∗The research has been partially supported by the Spanish Ministry of Science and InnovationGrant MTM2009-09440-C02-01 and by the COST Action IC0702.

31

SPO 2011 Jaca, September 13–16th 2011 COURSES AND CONFERENCES

Multi-class data exploration using spacetransformed visualization plots

Rida E. Moustafa1, Ali S. Hadi2, Jurgen Symanzik3

SUMMARY

Visualization of large data sets is computationally expensive. For this reason, envelop-ing methods have been used to visualize such data sets. Using enveloping methods,we visualize summary statistics of the data in the space transformed visualization(STV) plots, such as the traditional parallel coordinate plot (TPCP), instead of theactual data records. Existing enveloping methods, however, are limited only to theTPCP and they can also be misleading. This is because the parallel coordinates areparameter transformations and the summary statistics computed for the original datarecords are not preserved throughout the transformation to the parallel coordinatesspace. We propose enveloping methods that avoid this drawback and that can beapplied not only to the TPCP but also to a family of STV plots such as the smoothparallel coordinate plot (SPCP) and the Andrews plot. We apply the proposed meth-ods to the min-max, the quartiles, and the concentration interval envelopes (CINES).These enveloping methods allow us to visually describe the geometry of given classeswithout the need of visualizing each single data record. These methods are effectivefor visualizing large data sets, as illustrated for real data sets, because they mitigatethe cluttering effect in visualizing large-sized classes in the STV plots. Supplementalmaterials, including R-code, are available online to enable readers to reproduce thegraphs in this paper and/or apply the proposed methods to their own data [1].

References

[1] Rida E. Moustafa, Ali S. Hadi, Jurgen Symanzik (2011). Multi-Class DataExploration Using Space Transformed Visualization Plots. Journal of Computa-tional and Graphical Statistics 20(2), 298–315.

1dMining Technology, LLC, Ashburn, Virginia, [email protected]

2The American University in Cairo, New Cairo, [email protected]

3Department of Mathematics and Statistics,Utah State University, Utah, [email protected]

32

CONTRIBUTED

SESSIONS

CONTRIBUTED SESSIONS SPO 2011 Jaca, September 13–16th 2011

Modelling a bivariate counting process. Anapplication to the occurrence of extreme heat events

Abaurrea, J.1, Asın, J.1, Cebrian, Ana C.1

SUMMARY

This work studies the occurrence of extremes in a stochastic bivariate framework us-ing an approach based on the common Poisson shock model (CPSM). This modelis a bivariate point process with univariate marginal Poisson processes that takesinto account the dependence between them. One advantage of the CPSM is thatit can be represented by three independent Poisson processes. Due to this simplerepresentation, we can generalise the model to allow for time varying parametersand readily apply to real data. The required tools to fit and validate the model arepresented, including a new test to check the local conditional independence betweennon homogeneous Poisson processes. Among other extremes, the bivariate model isadequate to model heat waves. This is a complex phenomenon that cannot be prop-erly characterized by only the daily maximum temperature, and that can seriouslyaffect health, energy management and regional economies (catastrophic crop failures,physical damages, etc.). The series of extreme heat events in daily maximum andminimum temperatures in Huesca (Spain) is used to exemplify the modelling process.

Keywords: bivariate Poisson process, non homogeneous Poisson process, test ofindependence between point processes, heat waves analysis

AMS Classification: 60G70, 62M99, 62P12.

References

[1] Lieshout M.N.M. and Baddeley, A.J., (1999). Indices of dependence betweentypes in multivariate point patterns. Scandinavian journal of Statistics 26(4), 511-532.

[2] Lindskog F. and McNeil, A.J. (2003). Common Poisson shock models: appli-cations to insurance and risk modelling. ASTIN Bulletin 33, 209-238.

1Departamento de Metodos Estadısticos. Universidad de [email protected]

35

SPO 2011 Jaca, September 13–16th 2011 CONTRIBUTED SESSIONS

Development of a daily to hourly rainfalldisaggregation model

J. Abaurrea1, J. Asın1, A.C. Cebrian1, N. Gavın1

SUMMARY

The aim of this work is to develop a statistical model to disaggregate a daily precip-itation series into an hourly one, because it is the minimum resolution required bya hydrological-hydraulic model used to evaluate the likely changes in a small basinunder a climate change scenario.

In the Ebro basin there are some 15-minute precipitation gauging stations whichhave been recording data from 1997. These series are too short for fitting downscalingmodels able to generate local precipitation series in a climate change scenario. So, itwas necessary to use longer daily precipitation series and to provide a disaggregatingtool for generating the input to the hydrological model.

The proposed disaggregation model is made up of two components: the first is alogistic regression describing the precipitation occurrence every hour; the second isa generalized linear model with a gamma error that gives the hourly precipitationamount when it is positive.

This model has been succesfully validated and applied to eight 15-minute gaugingstations, representing different rainfall regimes in the Ebro basin. Its results comparefavourably with those obtained using the method by Mezghani and Hingray (2009).

Keywords: rainfall disaggregation, hourly precipitation, GLM.

AMS Classification: 62P12, 62J12, 62M10.

References

[1] Mezghani, A., Hingray, B. (2009). A combined downscaling-disaggregationweather generator for stochastic generation of multisite hourly weather variablesover complex terrain: Development and multi-scale validation for the Upper RhoneRiver basin. Journal of Hydrology volume(377), 245–260.

1Departamento de Metodos Estadısticos, Universidad de Zaragoza.gs [email protected]

36


On the convergence rates of multivariatehigher-order polynomial kernels

B. A. Afere1 F. O. Oyegue1

SUMMARY

One way of measuring globally the discrepancy between the estimated density f andthe true density f , in kernel density estimation, is the Asymptotic Mean IntegratedSquared Error (AMISE). In this paper, focus is on the derivations of the optimalbandwidth and asymptotic mean integrated squared error of higher order polynomialkernels of multivariate kernel density estimation. The consequence of the latter isthat it leads to faster rate of convergence, which is the speed at which the estimateddensity approaches the true density, compared to some of the rates in the literature,and also leads to bias reduction.

Keywords: Density estimation, AMISE, optimal bandwidth, higher order kernels,rate of convergence.

1Department of Mathematics and Statistics, Federal Polytechnic, Idah,Kogi State, [email protected]

37


A heuristic for identifying unknown agents in atransaction network∗

David Alcaide1, Joaquın Sicilia2, Miguel Angel Gonzalez Sierra3

SUMMARY

This paper deals with the problem of identifying unknown subject names in a trans-action network. To do it, the only information available is the knowledge of the namesof some subjects in the network; and certain records of past observations of trans-actions between all pairs of subjects. Such records offer us information about thefrequency (probability, intensity) of these transactions. The aim is to find the moresuitable identification of the unknown subjects, i.e., the identification with maximumfrequency (probability, intensity). A heuristic approach is proposed for solving thisprobabilistic problem and its performance is numerically illustrated.

Keywords: graph theory, probability, heuristic algorithms, assignment problems

AMS Classification: 90B80, 90C10

1Department of Statistics, Operations Research and Computer SciencesUniversity of La Laguna, [email protected]



∗This work is partially supported by the research project MTM2010-18591 from the SpanishMinistry of Science and Innovation.

38


Labour accessibility and residence attractiveness: aBayesian analysis based on Spatial interaction

models

Maria Pilar Alonso1, Asuncion Beamonte2, Pilar Gargallo3 ManuelSalvador4

SUMMARY

In this work we use a Poisson interaction gravity model with spatial effects thatallows us to joint measure the labour accessibility and the residence attractiveness ofa BSU, distinguishing between the attractiveness and impedance components. Theestimation process of the model is carried out using Bayesian tools based on the useof auxiliary mixture sampling. For illustration purposes, the methodology is appliedto a dataset containing information of commuters from the Spanish region of Aragon.

Keywords: Labour accessibility, Residence attractiveness, Commuting, Auxiliarymixture sampling, Bayesian inference, Spatial interaction models

AMS Classification: 62F15, 62H11, 62P25

1Facultad de Geografia. Universidad de [email protected]

2Facultad de Economia y Empresa. Universidad de [email protected]



39


Infinite time horizon crew scheduling modeling for atrain transportation problem

Jorge Amaya1, Hector Ramırez1, Paula Uribe1

SUMMARY

This work introduce a crew scheduling problem for train operations, based on a rota-tive schema, where weekly trips are fixed along the time, meaning that trips programdoesn’t vary along the weeks. Each schedule, generates a 0-1 medium/large size(hundreds to thousands of variables and constraints) optimization problem, but withcomplexity on constraints due to the lack of structure. The special feature of thismodel rests on the property of being an infinite horizon schedule, due to the rotativeschema, where every crew takes the place of the consecutive crew when a new weekstarts. The problem resolution is made through three steps: first, finding a feasiblesolution of infinite length, where schedules repeat in a rotative way between crews;then, an adapted local search is applied to improve the initial solution, in order toequilibrate the weekly working hours among crews and break the symmetry of theproblem; finally, drivers are assigned to the scheduled weeks, solving a flow problem.

Keywords: crew scheduling, integer programming, local search, heuristics.

AMS Classification: 90C10, 90C90, 90C59

1CMM-DIM, Universidad de Chile.Avda. Blanco Encalada 2120, piso 7Santiago de [email protected] [email protected]

[email protected]

40


Optimal Experimental Designs for Time SeriesModels

Mariano Amo-Salas1, Jesus Lopez-Fidalgo2

SUMMARY

Time Series models are a sort of nonlinear models where the observations are notindependent and the function which defines this correlation depends on the mean ofthe model. In this work, these models are studied from the framework of OptimalExperimental Design in order to obtain the best moments to perform the experiments.The model and the covariance function are expressed in a suitable form to applythe usual techniques of Optimal Experimental Design. The expression of the Fisherinformation matrix is provided for estimating the parameters of the model whenthey appear in the covariance function. Optimal designs for the simplest models arecomputed for different nominal values of the nonlinear parameter and their efficienciesare compared. Finally, more complex models are proposed.

Keywords: Time Series, Correlation, Optimal Design


1Department of Mathematics, University of Castilla-La Mancha. Institute ofApplied Mathematics in Science and [email protected]

2Department of Mathematics, University of Castilla-La Mancha. Institute ofApplied Mathematics in Science and [email protected]

41


On spectral and statistical analysis of heavy-tailedKolmogorov Pearson diffusions

Florin Avram1, Nikolai Leonenko2, Nenad Suvak3

SUMMARY

One dimensional diffusions are the most tractable class of stochastic processes. Theself-adjointness of the associated semigroup yields a spectral decomposition due toMcKean which has found many useful applications, for example in mathematicalfinance.

However, on non-compact state spaces, the spectrum of the generator will generallyinclude both a discrete and a continuous part, with the latter starting at a cutoffpoint related to the nonexistence of stationary moments, and the significance of thiscomplication for statistical estimation is not yet understood.

Motivated by this question, we consider here the problem of parameter estima-tion for a class of hypergeometric diffusions with heavy-tailed Pearson type invariantdistribution of inverse Gamma, Fisher-Snedecor, or Student type, which exhibit thespectral cutoff phenomena.

We propose, in the positive recurrent case, and assuming the existence of secondmoments, moments based estimators for the parameters (related to the orthogonalpolynomials) and prove their consistency and asymptotic normality.

Keywords: Diffusion process, Pearson equation, orthogonal polynomials, Methodof moments

AMS Classification: 60G10, 60J25, 60J60

1Universite de [email protected]

2Cardiff [email protected]

3University of [email protected]

42


Robustness and Density Power DivergenceMeasures

Ayanendranath Basu1, Abhijit Mandal1, Nirian Martin2, Leandro Pardo3

SUMMARY

This paper is motivated by a classical experiment presented in Woodruff et al. (1984)and Simpson (1989). In that example males flies were exposed either to a certaindegree of chemical to be screened or to control conditions and the responses are thenumbers of recessive lethal mutations observed among daughters of those files. Thedata are given by

0 1 2 3 4 5 6 7Observed (Control) 159 15 3 0 0 0 0 0Observed (Treated) 110 11 5 0 0 0 1 1

As in Simpson (1989), we will assume that the responses in the control group andthe treated group are random samples from the Poisson distributions with mean θ1and θ2 respectively. Our interest is in testing the hypothesis H0: θ1 ≥ θ2 againstH1 : θ1 < θ2. The apprehension is that the presence of the two large counts for thetreated group may make the the mean of the second group appear larger, althoughthis conclusion may not be supported by the rest of the data. Using Likelihood RatioTest (LRT) based on Maximum Likelihood Estimator (MLE) we get p-value = 0.0015and if we delete the two outliers (observations corresponding to observations 6 and 7in observed treated we get p-value = 0.1359. What is the reason for this discordance?The problem is that the MLE as well as the LRT are not robust procedures.

In this paper we consider Density Power Divergence introduced and studied inBasu et al. (1998) for estimation and we use them in the framework of hypothesistesting to overcome the problem pointed previously. Some theoretical results arepresented as well as a simulation study in order to study the robustness of the newprocedure in relation to the procedures based on MLE and LRT.

Keywords: density power divergence, robustness, tests of hypotheses

AMS Classification: 62F12, 62F05

1Indian Statistical [email protected], abhi [email protected]

2Carlos III University of [email protected]

3Complutense University of [email protected]

43


Asymptotic normality through factorial cumulantsand partitions identities

Konstancja Bobecka1 Pawe l Hitczenko2 Fernando Lopez-Blazquez3

Grzegorz Rempa la4 Jacek Weso lowski5

SUMMARY

We develop a relatively general approach to asymptotic normality through factorialcumulants. Factorial cumulants arise in the same manner from factorial moments,as (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a newidentity for ”moments” of partitions of numbers. As a result we show that the asymp-totic normality holds if factorial moments can be written in a suitable exponential-polynomial form. It appears that such a form is quite natural in many probabilisticmodels. Thus this general limiting result is used to (re)derive asymptotic normalityfor several models including classical discrete distributions, occupancy problems inseveral generalized (inverse) allocation schemes, including e.g. occupancy for distin-guishable or indistinguishable balls or random forests.

Keywords: Asympotic normality, factorial cumulants, allocation schemes, parti-tions of numbers, moments of partitions.

AMS Classification: 60F05, 05A17

1Wydzia l Matematyki i Nauk Informacyjnych, Politechnika Warszawska,Warszawa, [email protected]

2Department of Mathematics, Drexel University, Philadelphia, [email protected]

3Facultad de Matematicas Universidad de Sevilla, Sevilla, [email protected]

4Department of Biostatistics, Medical College of Georgia, Augusta, [email protected]

5Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa,[email protected]

44


Semiparametric estimation of a two-componentsmixture of regression models

Laurent Bordes1, Ivan Kojadinovic2, Pierre Vandekerkhove3

SUMMARY

We consider a two-component mixture of regression models where one component ispartially known while the other is unknown. More precisely we consider (Y,X) ∈R× Rp such that

Y =

{α0 + β′0X + σε0 with probability 1− π,α+ β′X + ε with probability π.

where α0, β0 and the density function (df) f0 of ε0 are known and σ ∈ (0,+∞),α ∈ R, β ∈ Rp, π ∈ (0, 1) and the df f of ε are the unknown parameters of themodel. This model extends a previous model proposed in [1]. First we show thatprovided that β 6= β0 the model parameters can be identified even if f is not aneven density function. Then considering n i.i.d. copies of (X,Y ) we propose someestimators of all the unknown parameters and we give their asymptotic behavior. Forthe functional part of the model we show that the covariance of the limit process canbe approximated by using a weighted bootstrap approach. Some simulation resultsillustrate our results.

Keywords: Semiparametric, mixture, regression

AMS Classification: 62G05, 62G20, 62J05

References

[1] L. Bordes, C. Delmas and P. Vandekerkhove (2006). Estimating a two-component mixture model when a component is known. Scand. J. Statist. 33(4),733–752.

1University of Pau - UMR CNRS [email protected]


3University of Paris-Est Marne la Vallee - UMR CNRS [email protected]

45


Extending the Classical Koziol-Green model byusing a copula function

Roel Braekers1, Auguste Gaddah2,

SUMMARY

In survival analysis, we are interested in the time until an event. However, dueto different practical reasons, we often do not fully observe this time. There is asecond independent random variable, a censoring time, which obscures the observationprocess and we only observe the smallest of both times and an indicator variablethat indicates which variable is the smallest. The classical approach to estimatethe distribution function for the time until an event under the assumption that thedistribution of the censoring time is informative for this time until an event is bythe Koziol-Green model. In this model, it is assumed that the survival function ofthe censoring time is a power of the survival function of the time until an event. Inthis talk, we generalize this model and assume a parametric function, depending ona parameter θ, to describe the relationship between the distribution functions of thetime until an event and the censoring time. Hereby we first show that this assumptionis equivalent to specifying a slide of a copula function between the observed lifetimeand the censoring indicator. Based on this equivalence, we propose a pseudo maximumlikelihood function to estimate the parameter θ. Furthermore we construct a semi-parametric estimator for the distribution function of the time until an event. Asresults, we first show the consistency and asymptotic normality of the parameter θ.Next we derive the weak convergence of the process associated to the semi-parametricestimator for the distribution function of the time until an event. In a simulationstudy, we investigate the finite sample performance of these estimators and finally weapply this model to a practical data set on survival with malignant melanoma.

Keywords: Copula, Consistency, Pseudo-likelihood, Random censorship, Weak con-vergence

AMS Classification: Primary 62N02, Secondary 62G20, 62G05

1Interuniversity Institute for Biostatistics and Statistical BioinformaticsUniversiteit Hasselt, Agoralaan 1, 3590 Diepenbeek, [email protected]

2Institut de Statistique, Universite Catholique de LouvainVoie du Roman Pays 20, 1348 Louvain-la-Neuve, [email protected]

46


Classification trees for the characterization of somearagonaise grapevine varieties

Jose Casanova1, Beatriz Lacruz2, Jesus M. Ortiz3

SUMMARY

Grapevine varieties characterization is an essential requirement since varieties pro-duction is limited in each cultivation area in Spain. Grapevine varieties are tradi-tionally described by their ampelographic measurements which usually present a highdegree of variability and non normal distributions. In order to analyze these data,classical statistical techniques as principal components and cluster analysis for theampelographic measurements averaged by variety are applied in the literature. Inthis work we propose to characterize 13 grapevine varieties found in the province ofHuesca (Spain) using classification trees over 27 ampelographic variables measured in20 leaves of each variety. Each leaf has been previously classified in its correspondingvariety by molecular techniques and the technique is applied to the whole data set.

Keywords: Classification trees

AMS Classification: 62H30, 62P10

1Departamento de Agricultura y Economıa AgrariaEscuela Politecnica Superior de HuescaUniversidad de Zaragoza (Spain)[email protected]

2Departamento de Metodos EstadısticosUniversidad de Zaragoza (Spain)[email protected]

3Departamento de Biologıa VegetalEscuela Tecnica Superior de Ingenieros AgronomosUniversidad Politecnica de Madrid (Spain)[email protected]

47


Two perspectives of design and modeling whensome independent variable is uncontrollable.

Vıctor Casero-Alonso1, Jesus Lopez-Fidalgo2

SUMMARY

We consider a linear regression model with two independent variables, one of themis uncontrollable but their values are known after the experiment is performed. Wecompare two ways of modeling this situation. On the one hand, there is a modelwith two explanatory variables (controllable and uncontrollable). On the other hand,there is a second model of simultaneous equations. Under restricted conditions, theD-optimal design is the same for both models. Under a general framework the D-optimal designs are different since the approaches are essentially different.

Keywords: Approximate design, Matrix information, D-optimal design, Simulta-neous equations, Conditionally restricted design

AMS Classification: 62K05, 62P20

1Escuela Tecnica Superior de Ingenieros Industriales (ETSII)Departamento de Matematicas (Estadıstica e I.O.)Avenida Camilo Jose Cela, 3 13071 Ciudad RealUniversidad de Castilla-La [email protected]

2Universidad de Castilla-La [email protected]

48


Free Completely Random Measures

Francesca Collet1, Fabrizio Leisen2, Antonio Lijoi3

SUMMARY

Free probability was initiated by Voiculescu around 1986 and it is a noncommutativeprobability theory in which the concept of independence of classical probability isreplaced by the concept of freeness [2]. In 1999 an important connection between freeand classical infinitely divisibility was established by Bercovici and Pata in form of abijection, mapping the class of classical infinitely divisible laws into the class of freeinfinitely divisible laws [1, 3].Our purpose is to derive, in the framework of free probability, a characterizationof typical objects in nonparametric Bayesian statistics. In particular, we will focuson the construction of the free infinitely divisible law corresponding to a classicalcompletely random measure.

Keywords: Bercovici-Pata bijection, free completely random measures, free prob-ability

AMS Classification: 60G57, 60E07, 46L54

References

[1] Barndorff-Nielsen, O. E. and Thorbjørnsen, S. (2006). Quantum inde-pendent increment processes. II. Springer, Berlin.

[2] D. Voiculescu (1986). Addition of certain noncommuting random variables. J.Funct. Anal. 66(3), 323–346.

[3] H. Bercovici and V. Pata (1999). Stable laws and domains of attraction infree probability theory. Ann. of Math. 149(3), 1023–1060.

1Departamento de Ciencia e Ingenierıa de Materiales e Ingenierıa Quımica,Universidad Carlos III de [email protected]

2Departamento de Estadıstica, Universidad Carlos III de [email protected]

3Dipartimento di Economia Politica e Metodi Quantitativi, Universita di [email protected]

49


Nonparametric predictive pairwise comparison withcompeting risks

Tahani Coolen-Maturi1

SUMMARY

In reliability, failure data often correspond to competing risks, where several failuremodes can cause a unit to fail. Maturi et al [1] introduced nonparametric predictiveinference (NPI) for competing risks, where interest is in the question which failuremode causes the next unit to fail. NPI is a statistical approach based on few as-sumptions, with inferences strongly based on data and with uncertainty quantifiedvia lower and upper probabilities. Recently, Coolen-Maturi & Coolen [2] consideredNPI for competing risks in the case of unobserved, re-defined, unknown or removedfailure modes. This paper presents NPI for pairwise comparison with competing risksdata, assuming that the different failure modes are independent. The focus is on thelower and upper probabilities for the event that the lifetime of a future unit from onegroup, say X, is less than the lifetime of a future unit from the second group, sayY , with different independent competing risks. The paper also shows how the twogroups can be compared given a particular failure mode.

Keywords: Pairwise comparison, competing risks, lower and upper probabilities,lower and upper survival functions, nonparametric predictive inference, right-censoreddata.

AMS Classification: 62N99, 62G99, 62N05.

References

[1] T.A. Maturi, P. Coolen-Schrijner and F.P.A. Coolen (2010). Nonparametric pre-dictive inference for competing risks. Journal of Risk and Reliability, 224(1), 11-26.

[2] T. Coolen-Maturi and F.P.A. Coolen (2011). Unobserved, re-defined, unknownor removed failure modes in competing risks. Journal of Risk and Reliability, toappear.

1Department of Mathematical Sciences, Durham University, Durham DH13LE, [email protected]

50


A Comparative Study of Bullwhip Effect in aMulti-Echelon Forward-Reverse Supply Chain

Debabrata Das1, Pankaj Dutta2

SUMMARY

Along with the forward supply chain organization needs to consider the impact ofreverse logistics due to social awareness, environmental benefits and economic ad-vantages. An important observation in a supply chain management, known as thebullwhip effect, refers to the phenomenon where orders to the supplier tend to havelarger variance than sales to the buyer (e.g., demand distortion), and the distortionpropagates upstream in an amplified form (e.g., variance amplification) (cf. [1]). Thequality and quantity of used products return to the collection points are uncertainin the reverse channel. Because of this, the systematic distortion is inevitable andbullwhip effect may occur at retailer, distribution and manufacturer level. In thispaper, first, we propose a system dynamics framework for a multi-echelon integratedforward-reverse supply chain network. Then, in the simulation study, we analyze theorder variation at both the retailer and distributor level and compare the bullwhipeffects of different logistics participants over time between the traditional forwardsupply chain and the integrated forward-reverse supply chain. Also, in the proposedmodel, a sensitivity analysis is performed to examine the impact of inventory adjust-ment time, cover time and collection rate of used products on the order variance andbullwhip effect.

Keywords: Reverse Supply Chain, Bullwhip Effect, Simulation, System Dynamics,Return Rate, Inventory Cover Time.

AMS Classification: 37M05, 90C31, 90B50

References

[1] Hau L Lee, V Padmanabhan, and Seungjin Whang (1997). The BullwhipEffect In Supply Chains. Sloan Management Review 38(3), 93–102.

1Research Scholar, Indian Institute of Technology, Bombay, Mumbai, [email protected]

2Assistant Professor, Indian Institute of Technology, Bombay, Mumbai, [email protected]

51


Likert and fuzzy scales:an empirical comparison through the MSE∗

Sara de la Rosa de Saa, Marıa Teresa Lopez, Marıa Asuncion Lubiano

SUMMARY

In dealing with random experiments related to questionnaires and surveys Likertscales are often employed to describe responses. These questionnaires and surveys areusually designed by considering a fixed-response format, so that possible responsesreflect in some senses the imprecision associated with most of the opinions or judge-ments. However, the natural subjectiveness as well as the realistic high diversityunderlying the responses are not well-captured with Likert scales.

In this paper, free-response format questionnaires or surveys based on the scaleof fuzzy numbers are to be considered. To compare the use of both scales from astatistical perspective an empirical study is to be presented. In this way, by usinga (generalized) mean squared error for fuzzy data, simulations are carried out togenerate randomly fuzzy numbers as potential responses. Some plausible criteriaare later applied to ‘Likertize’ these fuzzy numbers and the associated MSEs arecompared.

This introductory empirical analysis allows us to conclude that although the fuzzynumbered free -response format questionnaire/survey enables a much higher diversityand subjectiveness than Likert’s one, the mean value is more representative for the firstone than for the usual integer coding of the Likert in most of the situations. On onehand, the fuzzy numbers scale captures much better the diversity and subjectivenessof the responses and describes the imprecision in a much more accurate way and.On the other hand, the mean value leads in most of (in some cases even in all) thesimulations to a lower (squared) error in representing/estimating the responses withthe fuzzy than with the Likert scale.

Keywords: Likert scale, fuzzy numbers, generalized metric between fuzzy numbers

AMS Classification: 62A86, 62F86, 62-07

Departamento de Estadıstica e I.O. y D.M.,Universidad de Oviedo, 33071 Oviedo, [email protected], [email protected], [email protected]

∗The research has been partially supported by the Spanish Ministry of Science and InnovationGrant MTM2009-09440-C02-01 and by an STSM from the COST Action IC0702.

52


Statistical inference based on restricted sequentialorder statistics for weibull distribution with a

power trend model

M. Doostparast1, E. Velayati Moghaddam2,

SUMMARY

In engineering systems, it is usually assumed that the lifetime of the componentsare independent and identically distributed (iid). But, failing a components causesmore load on the remaining components. Thus, the distribution of the survivingcomponents would be changed (cf. [1]). For modeling this kind of systems, the theoryof sequential order statistics (SOS) may be used. Assuming the Weibull distributionfor the lifetime of the components and conditionally proportional hazard rates modelas a special case of SOS theory, the Maximum Likelihood estimates of the unknownparameters were obtained in different cases. A new model, called PTCPHM, asa generalization for iid case is proposed. Statistical inference including point andinterval estimates and the problem of hypothesis testing for PTCPHM are discussed.Finally, an illustrative example and a simulation study to carry out the performanceof the procedures obtained are given.

Keywords: Hypothesis testing, Likelihood Estimation, Proportional hazard rate,Sequential order statistics, Weibull model

AMS Classification: 62F03, 62N01, 62N03

References

[1] Balakrishnan, N., Beutner, E., Kamps, U. (2008). Order restricted inferencefor sequential k-out-of n systems. Journal of Multivariate Analysis 99, 1489–1502.

1Department of Statistics, School of Mathematical Sciences, Ferdowsi Univer-sity of Mashhad, [email protected]

2Department of Statistics, School of Mathematical Sciences, Ferdowsi Univer-sity of Mashhad, [email protected]

53


A proposed Markov model for predicting thestructure of a multi-echelon educational system in

Nigeria

Virtue U. Ekhosueh1 Augustine A. Osagiede2

SUMMARY

This paper is concerned with deriving, using logistic and Markov chain theoreticmethodologies, a transition model for a stable educational system in Nigeria. Theresulting transition model is the neo-stable imbedded Markov model. It is shown usingan entropy-based uncertainty metric that the neo-stable imbedded Markov model ispreferable to the stable imbedded Markov model in literature for long-term projectionusing dataset from a university.

Keywords: binomial logistic model; Markov model; multi-echelon educational sys-tem; Nigeria

AMS Classification: 60J20; 97B101Department of Mathematics, University of Benin,Benin City, [email protected]

2Department of Mathematics, University of Benin,Benin City, [email protected]

54


Analysis of Demographic and Health Survey Dataof Turkey with Bayesian Networks and Association

Analysis

Derya Ersel1, Suleyman Gunay2

SUMMARY

Data mining is a process of discovering new relationships, patterns and trends fromlarge databases. In this process many statistical methods can be used. Two of thesemethods are Bayesian Networks and association analysis. Bayesian Networks are usedto encode probabilistic relationships among random variables and they combine datainformation and experts knowledge about data [1]. In the literature, many learningalgorithms have been proposed to build Bayesian Networks. They can also be builtaccording to association analysis results [2]. Association analysis is used to extractsurprising and useful patterns from large databases. However, association analysisalgorithms generate many patterns even if the data set is very small. Therefore, thesepatterns should be eliminated with respect to their interestingness by using objectiveand subjective interestingness measures. Subjective measures can be established bymeans of Bayesian Networks. In this study, these two methods are used together toanalyze Demographic and Health Survey (DHS) 2008 data of Turkey.

Keywords: bayesian networks, association analysis, knowledge discovery, DHS

AMS Classification: 94C15, 90B15, 68P15

References

[1] JENSEN, F. V. (2001). Bayesian Networks and Decision Graphs. Springer-Verlag, New York.

[2] JAROSZEWICZ, S. and SIMOVICI, D. A. (2004). Interestingness of frequentitemsets using bayesian networks as background knowledge. In Proceedings of theKDD, 2004 , 178–186.

1Hacettepe University, Dept. of Statistics, 06800,Beytepe, Ankara, [email protected]

2Hacettepe University, Dept. of Statistics, 06800,Beytepe, Ankara, [email protected]

55


Linear combination of biomarkers to improvediagnostic accuracy in Prostate cancer

Luis Mariano Esteban1, Gerardo Sanz2, Angel Borque3

SUMMARY

The combination of multiple biomarkers in order to improve diagnostic accuracy isan important issue in Medicine. How to provide an optimal solution to this problemis a widely analyzed issue that has not got a global answer. In different papers,linear combinations of markers that maximize the Area under the Receiver Operatingcharacteristic Curve (ROC) have been proposed. However, none of them can beapplied in all posibles scenarios. Su and Liu [1] provide an optimal solution derivedunder multivariate normality that is not easy to verify in medical data. On the otherhand, nonparametric methods can be computationally intensives when the number ofbiomarkers is large[2]. In this work, we analyze the performance of two methods, astep by step algorithm [3] and the min-max combination [4] that have been recentlyproposed, in order to improve diagnostic accuracy in prostate cancer.

Keywords: biomarkers, ROC curve, linear combinations

AMS Classification: 62P10,62J99

References

[1] Su, J.Q. and Liu, J.S., 1993. Linear combinations or multiple diagnostic markers.J. Amer. Statist. Assoc., 88, 1350–1355.

[2] Pepe, M.S., Cai, T. and Longton, G., 2006. Combining Predictors for ClassificationUsing The Area under the Receiver Operating Characteristic Curve. Biometrics,62, 221–229.

[3] Esteban LM, Sanz G, Borque A, 2011. A step-by-step algorithm for combiningdiagnostic tests. Journal of Applied Statistics, 38(5), 899–911.

[4] Liu C, Liu A, Halabi S, 2011. A min-max combination of biomarkers to improvediagnostic accuracy. Stat Med. 30(16), 2005–2014.

1Escuela Universitaria Politecnica de La Almunia, Universidad de [email protected]

2Departamento de Metodos Estadısticos, Universidad de [email protected]

3Hospital Universitario Miguel Servet. [email protected]

56


Optimum Designs for Enzyme Inhibition Models:Algorithmic Approach.

Mercedes Fernandez-Guerrero1, Raul Martın-Martın2, Licesio J.Rodrıguez-Aragon2

SUMMARY

Enzyme kinetics study the rate of substrate that are transformed into products duringa reaction catalyzed by an enzyme [1]. The characterization of these processes is ofwide interest for the correct interpretation of the chemical mechanisms that take placeduring a chemical reaction.

An experimental design consists of a planned collection of points in a given spaceS×I where experimental observations are taken. In this work, the design criteria usedare D− and A−optimality. The D−optimal criterion minimizes the volume of the

confidence ellipsoid of the parameters and is given by φD[M(ξ; θ)] = detM(ξ; θ)−1/k

,where k is the number of parameters in the model. The A-optimal criterion minimizesthe sum of the variances of the parameters and is given by φA[M(ξ; θ)] = tr M(ξ; θ)

−1.

The Wynn-Fedorov algorithm to compute optimal designs used in this work addsa new point to an initial design based on the information provided by the EquivalenceTheorem at each iteration [2]. Its application to multifactor models, as the proposed,shows the advantages and disadvantages of the algorithm.

Keywords: Optimum Designs, Enzyme Inhibition, Wynn-Fedorov Algorithm


References

[1] Illanes, A. (2008). Enzyme Biocatalysis: Principles and Applications. Springer.

[2] Fedorov, V. V., Hackl, P. (1997). Model-Oriented Design of Experiments.Lecture Notes in Statistics, Spinger.

1,2,3Universidad de Castilla-La Mancha,Instituto de Matematica Aplicada a la Ciencia y a la Ingenierı[email protected]

[email protected]

[email protected]

57


An study of some frailty models

Fernandez-Ponce, J.M.1, Palacios-Rodrıguez, F.1, Rodrıguez-Grinolo, R.2

SUMMARY

Different sufficient conditions for stochastic comparisons between random vectors havebeen described in the literature. In particular, comparisons between frailty modelsassuming independence for the baseline survival functions and the corresponding en-vironmental parameters (see ([1]),[2],[3],[4],[5], among others). In this work, we studysome distributions and their properties for these models.

Keywords: Copula, Frailty Models, Simulation

AMS Classification: 60E15; 60K10; 62P05

References

[1] Gupta, R.C.. and Gupta, R.D. (2010). Random effect bivariate survival mod-els and stochastic comparisons. Journal of Applied Probability, 47, 426-440.

[2] Khaledi, B.E. and Shaked, M. (2010). Stochastic comparisons of mulitivariatemixtures. J. Multivariate Anal., 101,10, 24862498.

[3] Li, X. and Da, G. (2010). Stochastic comparisons in multivariate mixed modelof proportional reversed hazard rate with applications. Journal of MultivariateAnalysis, 101, 1016–1025

[4] Misra, N., Gupta, N. and Gupta,R.D. (2009). Stochastic comparisons ofmultivariate frailty models. Journal of Statistical Planning and Inference, 139,2084–2090.

[5] Mulero, J.; Pellerey, F. and Rodrıguez-Grinolo, R. (2010). Negative ag-ing and stochastic comparisons of residual lifetimes in multivariate frailty models.Journal of Statistical Planning and Inference, 140, 1594–1600.

1Departamento de Estadıstica e I.O.Universidad de Sevilla (Spain)[email protected],[email protected]

2Departamento de Economıa, Metodos Cuantitativos e Historia EconomicaUniversidad Pablo de Olavide, Sevilla (Spain)[email protected]

58


Response-adaptive designs based on the Ehrenfesturn

Arkaitz Galbete1; Jose Antonio Moler2 and Fernando Plo3

SUMMARY

Response driven adaptive designs have received an increasing interest in the statisticalliterature due to their applications in industry, economics, medicine, etc. But it is inthe framework of clinical trials where they have known their maximum development,see, for instance, [1]. Under a response adaptive design the last patient is randomlyallocated to a treatment using the previous information, that is, the previous responsesand allocations of patients. In this way, some ethical goals can be achieved, skewingthe number of allocations to the treatment which is showing the best performance,and preserving, to some extent, the randomness of the allocations. Urns appear asan appropriate probabilistic tool to model this kind of designs.

In this paper we describe a family of response-adaptive designs based on the Ehren-fest urn model, where the previous responses of patients are used in the transitionprobabilities of the urn, and therefore in the next allocation. We study some operat-ing characteristics of these designs, such as the power of the usual inferential tests,the variability of the proportion of allocations, the expected failure rate or the targetallocation and we compare them with other well-known response-adaptive designs.

Keywords: Response-adaptive designs, Ehrenfest urn.

AMS Classification: 60C05, 60F05

References

[1] Hu, F. and Rosenberger, W. F. (2006) The theory of response-adaptive ran-domization in clinical trials. Wiley, New York.

1,2Department Estadıstica e Investigacion OperativaUniversity Publica de NavarraPostal address Campus Arrosadia s/n, 31006, Pamplona, [email protected], [email protected]

3Department Metodos estadısticosUniversity ZaragozaPostal address Pedro Cerbuna 12, 50009, Zaragoza, [email protected]

59


Maximum likelihood and bayesian estimates andprediction for geometric distribution based on

δ-records

R. Gouet1 F.J. Lopez2, L.P. Maldonado2, G. Sanz2

SUMMARY

We propose maximum likelihood and Bayes estimators for the parameter of theGemoetric distribution based on δ-records. The Bayes estimates are obtained us-ing informative and non-informative prior distributions. Empirical Bayes estimatesare also obtained. In order to evaluate the different estimates we calculate the meansquare errors through Monte Carlo simulations and compare them with the corre-sponding estimatros based on usual records [1]. Also, Bayesian prediction of thefuture record values are obtained and discussed.

Keywords: δ-Records, Bayes Estimation, Bayes prediction, Empirical Bayes, Geo-metric Distribution.

AMS Classification: 62F15, 62M20, 60G70

References

[1] Doostparast, M. and Ahmadi, J. (2006). Statistical analysis for geometricdistribution based on records. Computers and Mathematics with Applications, 52,905–916.

1Dpto. Ingenierıa Matematica and CMM (UMI 2807, CNRS), Universidad [email protected]

2Dpto. de Metodos Estadısticos. Universidad de Zaragoza (Spain)[email protected], [email protected], [email protected]

60


Geometric Records

Raul Gouet1, F. Javier Lopez2, Gerardo Sanz2

SUMMARY

We consider in this communication the long-term behavior of geometric records from asequence {Xn}n≥1 of independent, nonnegative, random observations, with commoncontinuous distribution function F . Give a parameter k > 1, the n-th observationXn is a geometric record if Xn > kmax{X1, . . . , Xn−1}, that is, if Xn is k timesgreater than all preceding observations. This concept was introduced by Eliazar in[2], where the question of waiting times was addressed. We study the number Nn ofgeometric records among X1, . . . , Xn, and show that Nn increases to a finite randomlimit N∞, for very light-tailed F . For medium and heavy-tailed F , we prove thatNn diverges to infinity, establish its growth rate and give conditions for asymptoticnormality. We also analyze the values of geometric records, pointing out a relationshipwith models of paralyzable counters in particle physics. Our results are presented ina discrete-time setting but we show how they can be translated to continuous timePoissonian systems. Examples of applications to common families of distributions,such as Frechet systems, are also provided.

Keywords: Records; Geometric records; Limit Theorems; Type II counters

AMS Classification: 60G70, 60F05, 60F15.

References

[1] Arnold, B.C., Balakrishnan, N., Nagaraja, H. N. (1998). Records. Wiley,New York.

[2] Eliazar, I. (2005). On geometric record times. Phys. A 348, 181–198.

1Dpto. Ingenierıa Matematica and CMM (UMI 2807, CNRS), Universidad deChile, Av. Blanco Encalada 2120, 837-0459, Santiago, Chile. Supported bygrants PFB-03-CMM, Fondecyt 1090216 and MTM2010-15972 of [email protected]

2Dpto. Metodos Estadısticos and BIFI, Facultad de Ciencias, Universidad deZaragoza. C/ Pedro Cerbuna, 12. 50009 Zaragoza, Spain. Supported bygrant MTM2010-15972 of [email protected]; [email protected]

61


On the structure of near-record values

Raul Gouet1, F. Javier Lopez2, Gerardo Sanz2

SUMMARY

Near-records of a sequence are observations lying within a fixed distance of the cur-rent record [1]. In this work we study the structure of near-record values, showingthat they can be seen as a nonhomogeneous Poisson cluster process. Based on thisrepresentation we derive some properties of near-record values. We also show hownear-records can be used in inferential procedures, improving classical estimationsbased on record values only.

Keywords: Records, near-records, cluster Poisson process, maximum likelihood es-timation.

AMS Classification: 60G70, 60G55, 62F10.

References

[1] Balakrishnan N, Pakes AG, Stepanov A (2005). On the number and sumof near-record observations. Adv Appl Probab 37, 765-780.

1Dpto. Ingenierıa Matematica and CMM (UMI 2807, CNRS), Universidad deChile, Av. Blanco Encalada 2120, 837-0459, Santiago, Chile. Supported bygrants PFB-03-CMM, Fondecyt 1090216 and MTM2010-15972 of [email protected]

2Dpto. Metodos Estadısticos and BIFI, Facultad de Ciencias, Universidad deZaragoza. C/ Pedro Cerbuna, 12. 50009 Zaragoza, Spain. Supported bygrant MTM2010-15972 of [email protected]; [email protected]

62


A least squares estimation method for highheteroscedastic linear models

Ali S. Hadi1, Beatriz Lacruz2, Ana Perez-Palomares2

SUMMARY

In this work we propose an estimation method for a linear model with heteroscedas-ticity. The approach we propose presents an important difference with the usualtechniques, since we are interested in approximating the inverse of the variance whichwe suppose that it is a smooth function to be approximated by a polynomial. Then,we apply a restricted least squares criterium to estimate all the parameters involvedin the model.

Several simulation studies show that the method works well under different highlevels of heteroscedasticity. Moreover, in some particular cases, which correspond toa severe level of heteroscedasticity, theoretical results about the consistency and theasymptotic efficiency of the method have been obtained.

Keywords: Linear regression, heteroscedasticity, restricted least squares.

AMS Classification: 62J05, 62J20

1Department of Mathematics, American University in Cairo, (Egypt)[email protected]

2Departamento de Metodos Estadısticos, Universidad de Zaragoza, (Spain)[email protected], [email protected]

63


A Bootstrap Modification of the MultivariateBoosting Algorithm in KDE

Ishiekwene, C. C.1

SUMMARY

In this paper, a modified multivariate boosting algorithm in Kernel Density Estima-tion, KDE, is presented. It has the advantages of been easily computed/implementedand avoids the rigors of computation of the weight function by using the Bootstrap inplace of the Leave-One-Out function of Mazio and Taylor (2004). This new algorithmalso achieves the same goal of bias reduction which in turn translates to a reductionin the mean integrated squared error (MISE). A Bivariate sample is used to illustratethis new algorithm and the results compared.

Keywords: Multivariate, Boosting, Bootstrap, Leave-one-out, Bias, MISE, Bivari-ate.

AMS Classification: 62F40, 62G081Department of Mathematics, Faculty of Physical Sciences, University ofBenin, [email protected]

64


Simulating random variables with Lindley orPoisson–Lindley distribution

P. Jodra1

SUMMARY

We provide algorithms to generate random variables with Lindley, Poisson–Lindley,or zero-truncated Poisson–Lindley distributions. Our procedures are based on thefact that the quantile functions of these probability distributions can be expressed inclosed form in terms of the so-called negative branch of the Lambert W function. Werecall that the Lambert W function is a multivalued complex function defined as thesolution to the equation W (z) exp (W (z)) = z, where z is a complex number; the realbranch taking on values in (−∞,−1] is called the negative branch.

Our methods are more efficient than the algorithms proposed by Ghitany andAl-Mutairi [1] and Ghitany et al. [2, 3]. More precisely, our algorithms reduce theexecution time approximately 20% in the cases of Lindley distributions and more than250% in the cases of Poisson–Lindley distributions (cf. Jodra [4] for more details).

Acknowledgments. This research has been funded by DGA (Grupo PDIE) and by Vicerrec-

torado de Investigacion (Universidad de Zaragoza) project 226/128.

Keywords: Lindley distribution, Lambert W function, Simulation

AMS Classification: 65C05, 33B30

References

[1] M.E. Ghitany, D.K. Al-Mutairi (2009). Estimation methods for the discretePoisson–Lindley distribution. J. Stat. Comput. Sim. 79(1), 1–9.

[2] M.E. Ghitany, B. Atieth, S. Nadarajah (2008). Lindley distribution and itsapplication, Math. Comput. Simul. 78(4), 493–506.

[3] M.E. Ghitany, B. Atieth, S. Nadarajah (2008). Zero-truncated Poisson–Lindley distribution and its application. Math. Comput. Simul. 79(3), 279–287.

[4] P. Jodra (2010). Computer generation of random variables with Lindley orPoisson–Lindley distribution via the Lambert W function. Math. Comput. Simul.81(4), 851–859.

1Dpto. de Metodos EstadısticosUniversidad de Zaragoza (Spain)[email protected]

65


The Speed of Random Walks on Trees and ElectricNetworks

Mokhtar Konsowa1, Fahimah Al-Awadhi2

SUMMARY

The speed of the random walk on a tree is the rate of escaping its starting point,(cf. [1]). This depends on the way the branching occurs, for example if the averagenumber of branching is large then the speed is more likely to be positive. This, onsome models of random trees, is determined by using the hitting times of consecutivelevels of the tree (cf. [2]).

Keywords: Random walk, speed, electric network, resistance.

AMS Classification: 60J20, 05C05

References

[1] P. Doyle and L. Snell (1984). Random walks and electric networks. The CarusMathematical Monographs. Mathematical Association of America. Washington,D.C..

[2] M. Konsowa (2009). On the Speed of Random Walks on Random Trees. Statis-tics and Probability Letters, 79, 2230–2236.

1Department of Statistics and Operations Research, Faculty of Science,Kuwait University, P. O. Box 5969, Safat 13060, [email protected]

2Department of Statistics and Operations Research, Faculty of Science,Kuwait University, P. O. Box 5969, Safat 13060, [email protected]

66


Family of estimators of population variance insuccessive sampling

Nursel Koyuncu1

SUMMARY

Successive sampling consists of selecting sample units on different occasions such thatsome units are common with samples selected on previous occasions. We considersampling on two occasions from a finite population of size N. Associated with the ithunit are, the study variable, and auxiliary variable. Note that on the first occasion,the study variable y is called the auxiliary variable x. Using simple random sampling,units are selected on the first occasion. A random sub sample of units are retained foruse on the second occasion, while a fresh simple random sample of units are drawnon the second occasion from the remaining units of the population. In this scheme,drawing sample at different time point gives more reliable estimates than one-stagesampling. We can take into account the change of the characteristics over differentoccasions. In this paper we have intended to improve the precision of variance esti-mates at the current occasion. We have proposed a family of estimators of populationvariance and the expressions of bias and mean square error are derived in successivesampling. To analyze its properties we have carried out an empirical study based onreal populations.

Keywords: ratio estimator, mean square error, successive sampling.

AMS Classification: 62D05

References

[1] Koyuncu N. Kadilar, C.(2010). On Improvement in Estimating PopulationMean in Stratified Random Sampling. Journal of Applied Statistics 37(6), 999–1013.

[2] Singh, H.P., Tailor R., Singh S., Kim J.M., (2011). Estimation of PopulationVariance in Successive Sampling. Qual Quant 45, 477–494.

1Hacettepe University Statistics Department [email protected]

67


To obtain the number of hidden nodes in ELMmethodology

Beatriz Lacruz1, David Lahoz2, Pedro M. Mateo1

SUMMARY

The Extreme Learning Machine (ELM) is a recent algorithm for training single-hiddenlayer feedforward neural networks (SLFN) which has shown promising results whencompared with other usual tools. ELM randomly chooses weights and biases of hid-den nodes and analytically obtains the output weights and biases. In this work weintroduce an ELM algorithm that uses a micro genetic algorithm in order to generatethe hidden weights and biases of the SLFN, as well as the ELM methodology forobtaining the output weights. It minimizes simultaneously the approximation errorMSE and the number of hidden nodes to conduct the training and it is able to obtainthe appropriate number of hidden nodes as well as the associated weights and biasesvia a new strategy based on regression for which different strategies are tested. Theperformance of our approaches is compared with the original ELM algorithm andsome of its competitors in a wide set of problems usually found in the literature.

Keywords: MLP Neural Networks, Evolutionary Algorithms, Extreme LearningMachine, Multiple Objective Programming, Linear Regression

AMS Classification: 82C32, 90C29, 90C59, 62-07, 92B20

References

[1] Coello, C. A., Lamont, G. B., and Van Veldhuizen, D. A. (2007). Evolu-tionary Algorithms for Solvng Multi-Objective Problems, 2nd Edition. Springer.Berlin.

[2] Huang, G. B., Zhu, Q.Y. and Siew, C.K. (2006). Extreme learning machine:Theory and applications. Neurocomputing 70(1-3), 489–501.

[3] Lacruz, B., Lahoz, D., and Mateo, P.M. (2011). A bi-objective micro geneticextreme learning machine. . IEEE SSCI11 (HIMA), Paris, France, 68 – 75.

1Departamento de Metodos Estadısticos, Universidad de Zaragoza (Spain)[email protected],[email protected],[email protected]

68


CID sequences and Bayesian non parametrics

Fabrizio Leisen1,

SUMMARY

Conditional identity in distribution ([1]) is a new type of dependence for randomvariables, which generalizes the well-known notion of exchangeability. In Bassetti,Crimaldi, Leisen ([2]) a class of random sequences, called Generalized Species Sam-pling Sequences, is defined and a condition to have conditional identity in distributionis given. In particular, a class of generalized species sampling sequences that are con-ditionally identically distributed is introduced and studied: the Generalized Ottawasequences (GOS). Species sampling sequences is an important tool in Bayesian nonparametrics. Indeed, many popular Bayesian Nonparametric priors can be character-ized in terms of exchangeable species sampling sequences. One example is the DirichletProcess prior, that has been increasingly used for modeling purposes in mixture ofDP hierarchical models. However, in some applications, the implied exchangeabilityassumption may not be considered appropriate. In the GOS family it is available aspecies sampling sequence, characterized by a tractable predictive probability func-tion, and with weights driven by a sequence of independent Beta random variables.We discuss some of the properties that can be useful in applications, and we compareour findings with wellknown properties of the DP and the two parameters Poisson-Dirichlet process. We detail on Markov Chain Monte Carlo posterior sampling, andillustrate the behavior of such priors.

Keywords: Conditionally Identically Distributed Sequences, Species Sampling, BayesianNon Parametrics, Generalized Ottawa Sequences

AMS Classification: 62C10, 62G57

References

[1] Berti P., Pratelli L. and Rigo P. (2004). Limit Theorems for a Class ofIdentically Distributed Random Variables. Annals of Probability 32, 2029–2052.

[2] Bassetti F., Crimaldi I. and Leisen F. (2010). Conditionally identically dis-tributed species sampling sequences. Advances in applied probability 42, 433–459.

1Universidad Carlos III de [email protected]

69


The number of records in geometric samples∗

Lopez-Blazquez, Fernando,1 Salamanca-Mino, Begona2

SUMMARY

Records are left to right local maxima of a sequence of numbers. Counting the numberof records in random sequences is a problem of interest in several applied areas likeHydrology, Climatology, Finances, Computing Sciences, etc. It is well known that thedistribution of the number of records in a random permutation and in the case of iidsamples from an absolutely continuous parent can be written in terms of the Stirlingnumbers of the first kind. In the latter case it is remarkable that the distribution of thenumber of records does not depend on the parent distribution. For discrete parents,the situation is more complicated due to ties and to the fact that the distribution ofthe number of records depends on the parent distribution.

In this work, we study the distribution of the number of records (ordinary andweak) in iid samples from geometric distributions. Although some asymptotic resultsabout these distributions have been studied before by some authors, little is knownabout the exact distributions. Our main result shows that the distribution of thenumber of records can be written in terms of the q-Stirling numbers of the first kind.We also study the exact distribution of record times and its connection to non-centralq-Stirling numbers. The key for the obtention of these results is a new representationof (non-central) q-Stirling numbers of the first kind as a multiple Jackson integral.

Keywords: records, q-calculus, q-Stirling numbers, Jackson Integral

AMS Classification: 60C05, 05A30

1,2Dpto. Estadıstica e I.O.Facultad de Matematicas.Universidad de Sevilla.Reina Mercedes, s/n.41012 Sevilla, [email protected]

[email protected]

∗This reseach has been supported by grants MTM2010-16949 and FQM5849.

70


Logic regression model versus classical linear andlogistic regression models

Magdalena Malina1

SUMMARY

We consider a biological problem of locating multiple interacting genes. Logic regres-sion ([1]) is a regression method, specifically aimed at detecting high order interactionsin genetic data. The method attempts to construct predictors as Boolean combina-tions of dummy variables coding marker genotypes. The method searches for thesecombinations of predictors in the entire space of such combinations, which are repre-sented by logic binary trees. When there are many genes however, then the multipletesting problem arises and in a classical model selection criteria we need an additionalpenalty for model dimension ([2]). In Bayesian versions the problem of the penaltychoice is replaced by a problem of proper selection of prior distributions.

We describe theoretically constraints under which the logic regression is moreeffective in detection of complex interactions of variables than the classical linearregression. We perform a comparative analysis of powers of these methods with thelevel of FWER fixed. Considering the problem of detection of interacting genes asa problem of multiple testing, we show theoretically that logic regression may leadto a larger power than the standard methods based on a linear or logistic regressionmodel.

Keywords: logic regression, model selection, multiple testing

AMS Classification: 62J05, 62J15

References

[1] I. Ruczinski, C. Kooperberg and M. LeBlanc (2003). Logic regression.J. Comput. Graphical Statist. 12(3), 474–511.

[2] M. Bogdan,J. K. Gosh and M. Zak-Szatkowska(2008). Selecting explana-tory variables with the modified version of Bayesian Information Criterion. Qualityand Reliability Engineering International. 24 627–641.

1Mathematical Institute, Wroc law University,pl. Grunwaldzki 2/4, 50-385 Wroc [email protected]

71


Phi-divergence test statistics for loglinear modelssubject to constraints of likelihood ratio order

Nirian Martin1, Raquel Mata2, Leandro Pardo2

SUMMARY

In the analysis of loglinear models the assessment of the goodness-of-fit of an estimatedloglinear model involves determining the discordance between observed and estimatedfrequencies using a phi-divergence test statistic (see Pardo 2006, Martin and Pardo(2008)). In this paper we present some results in relation to the phi-divergence teststatistics in loglinear models when we have models with inequality constraints. Sometheoretical as well simulated results are presented.

Keywords: Phi-divergence measures, Loglinear modes, Likelihood Ratio Order

AMS Classification: 62F12, 62F05

References

[1] Martin, N. and L. Pardo (2008) New families of estimators and test statisticsin log-linear models. Journal of Multivariate Analysis, 99(8), 1590-1609.

[2] Pardo, L. (2006). Statistical Inference Based on Divergence Measures. Statistics:series of Textbooks and Monograhps. Chapman & Hall / CRC.

[3] Silvapulle, M. and Sen. (2005). Constrained statistical inference. Inequality,order, and shape restrictions. Wiley Series in Probability and Statistics. Wiley-Interscience (John Wiley & Sons)

1Department of Statistics,Carlos III University of Madrid,Calle Madrid, 126 - 28903 Getafe (Madrid), [email protected]

2Department of Statistics and O.R. I,Complutense University of Madrid,Plaza De Ciencias, 3 - 28040, Madrid, [email protected]

[email protected]

72


The problem of random generation of non-additivemeasures∗

P. Miranda1, E. F. Combarro2, I. Dıaz2

SUMMARY

Non-additive measures are a generalization of classical probability measures in whichadditivity is removed and monotonicity is imposed instead. They have become animportant tool in many different fields, as Decision Theory, Combinatorics, and so on(see [1] for a review on fuzzy measures).

An interesting problem arising in the practical use of non-additive measures is theproblem of identification of the non-additive measure modeling a concrete situation.Many different algorithms have been proposed in order to cope with this problem. Inorder to study whether a procedure works properly, we need to generate non-additivemeasures in a random way. This is the problem that we treat in this paper.

The problem of generating in a uniform way points in a polytope is in general acomplex problem. In the case of non-additive measures, we will use the particularstructure of this polytope. First, we will use the fact that it is an order polytope, sothe problem can be stated in terms of the subjacent poset, and it can be proved thatthe problem reduces to generate randomly a linear extension in the poset. Anotherpossibility is to use the symmetrical structure of the subjacent poset.

Keywords: Non-additive measure, order polytope, random generation, linear ex-tension.

AMS Classification: 28E10, 52B11, 65Y20.

References

[1] M. Grabisch and T. Murofushi and M. Sugeno (2000). Fuzzy Measures andIntegrals- Theory and Applications, Physica-Verlag.

1Complutense University of [email protected]

2University of [email protected], [email protected]

∗This research has been supported in part by grant numbers MTM2009-10072 and BSCH-UCM910707, and by MEC and FEDER grant TIN2010-14971.

73


Some contributions to the class of controlledtwo-sex branching processes

Manuel Molina1, Manuel Mota2, Alfonso Ramos3

SUMMARY

Inside the general context of stochastic modelling, the branching process theory pro-vides mathematical models to describe the probabilistic evolution of systems whosecomponents after certain life period reproduce and die. It is an active research areaof both theoretical interest and applicability to several fields. In particular, with thepurpose to model the probabilistic evolution of populations where females and malescoexist and form couples, some classes of two-sex branching processes have been stu-died, see for details [1] or [2]. It can be stated that significant efforts have been maderegarding controlled branching processes with asexual reproduction. Now similar e-fforts should be made to develop controlled processes where reproduction is bisexual.In an attempt to contribute some solution to this problem a new class of controlledtwo-sex branching processes has been introduced in [3]. In addition to its theoret-ical interest, this class of processes also has clear practical implications, especiallyin population dynamics. In this work, we continue the research about such a classof two-sex processes. We investigate several probabilistic questions and we considersome inferential questions. By way of illustration, simulated examples are presented.

Keywords: Branching processes, two-sex processes, controlled processes.

AMS Classification: 60J80

References

[1] D.M. Hull (2003). A survey of the literature associated with the bisexual Galton-Watson branching process. Extracta Mathematicae 18, 321–343.

[2] M. Molina (2010). Two-sex branching process literature. Lectures Notes inStatistics 197, 279–293.

[3] M. Molina, M. Mota and A. Ramos (2011). Two-sex branching models withrandom control on the number of progenitor couples. Methodology and Computingin Applied Probability , DOI 10.1007/s11009-010-9167-x.

1, 2, 3Department of Mathematics, University of Extremadura, [email protected], [email protected], [email protected]

74


The powers of the stochastic Gompertz diffusionprocess: Statistical inference

A. Nafidi1, R. Gutierrez2, R. Gutierrez-Sanchez2 E. Ramos2

SUMMARY

This study concerns the powers of the Gompertz diffusion process obtained fromthe homogeneous Gompertz diffusion model studied in (cf. [1], [2]). Firstly, it isshown that the power of a Gompertz process is also a Gompertz process. Then, theprobabilistic properties of the process thus defined are determined, as the analyticalexpression of the pdfs and the moments. Finally, based on the methodology estab-lished in (cf. [3]), we study statistical inference in this process, using the maximumlikelihood method in discrete sampling of the process.

Keywords: Gompertz model, Trend fonctions, Inference in diffusion process

AMS Classification: 60J60, 62M05

References

[1] Gutierrez, R., Gutierrez Sanchez, R., Nafidi, A. (2006). A. Electricityconsumption in Morocco: Stochastic Gompertz exogenous factors diffusion anal-ysis. Applied Energy 83, 1139-1151.

[2] Ferrante L, Bompade S, Possati L, Leone L, Montanari MP. (2005). Astochastic formulation of the Gompertzian growth model for in vitro bactericidadkinetics: parameter estimation and extinction probability. Biometrical Journal 47(3), 309-318.

[3] Gutierrez, R., Gutierrez Sanchez, R., Nafidi, A. (2009). Modelling andforecasting vehicle stocks using the trends of stochastic Gompertz diffusion models:The case of Spain. Appl. Stochastic Models Bus. Ind. 25, 385405.

1Nafidi A., LAMSAD. Ecole Superieure de Technologie- BerrechidB.P: 218, Berrechid, Universite Hassan 1er, [email protected]

2Gutierrez R., Gutierrez-Sanchez R.Department of Statistics and Operations Research, University of GranadaCampus de Fuentenueva s/n, 18071 Granada, [email protected], [email protected], [email protected]

75


A Bayesian Model for Longitudinal Circular Data

Gabriel Nunez Antonio1, Eduardo Gutierrez Pena2,

SUMMARY

The analysis of short longitudinal series of circular data may be problematic and tosome extent has not been completely developed. In this paper we present a Bayesiananalysis of a model for such data. The model is based on a radial projection onto thecircle of a particular bivariate normal distribution. Inferences about the parametersof the model are based on samples from the corresponding joint posterior densitywhich are obtained using a Metropolis-within-Gibbs scheme after the introduction ofsuitable latent variables. The procedure is illustrated both using a simulated data setand a real-data set previously analyzed in the literature.

Keywords: circular data, longitudinal data, Gibbs sampler, latent variables, mixed-effects linear models, projected normal distribution.

AMS Classification: 62F15, 62H11, 62-07

1Department of Statistics, University Carlos III of Madrid, [email protected]

2Department of Probability and Statistics, IIMAS-UNAM, [email protected]

76


A decision model for a newsvendor inventoryproblem with an extrordinary order∗

Valentın Pando1, Luis A. San-Jose2, Juan Garcıa-Laguna3, Joaquın Sicilia4

SUMMARY

This work presents a newsvendor inventory model with two ordering opportunities:the regular order and an extraordinary order. We suppose that the size of the emer-gency order depends on the behavior of the customers and it is automatically de-termined as a variable fraction of the extent of shortage in the inventory. Moreconcretely, the backlogged demand rate is described by a non-increasing cosinusoidal-type function with respect to the amount of shortage. In the model studied here, theobjective is to maximize the expected total profit for the period, when the demandfollows an exponential distribution. The uniqueness and existence of optimal policiesare proved and, by using closed-form expressions, we determine the optimal lot sizeand the maximum expected profit. This work extends several newsvendor inventorymodels proposed in the literature.

Keywords: newsvendor model, backlogged demand rate, maximum expected profit

AMS Classification: 90B05

1Department of Statistics and Operations ResearchUniversity of Valladolid, [email protected]

2Department of Applied MathematicsUniversity of Valladolid, [email protected]

3Department of Statistics and Operations ResearchUniversity of Valladolid, [email protected]

4Department of Statistics, Operations Research and ComputationUniversity of La Laguna, [email protected]

∗This work is partially supported by the research project MTM2010-18591 from the SpanishMinistry of Science and Innovation.

77


Landmark Prediction of Long Term SurvivalIncorporating

Short Term Event Time Information

Layla Parast1, Su-Chun Cheng2, Tianxi Cai3

SUMMARY

In recent years, a wide range of markers have become available as potential tools forsignaling progression or risk of disease. In addition to these markers, it has oftenbeen argued that short term outcome information may be very helpful in predictinglong term disease outcomes. When such information is available, it would be desir-able to combine this along with predictive markers to improve the prediction of longterm outcomes. Most existing methods for incorporating censored short term eventinformation in predicting long term survival focus on modeling the disease processand are derived under restrictive parametric models in a multi-state survival setting.When such model assumptions fail to hold, the resulting prediction of long term out-comes may be invalid or inaccurate. In this paper, we propose to incorporate shortterm event time information up to a landmark point along with baseline covariatesvia a flexible varying-coefficient model. To evaluate the performance of the result-ing landmark prediction rule, we propose robust non-parametric procedures to makeinference about the accuracy measures and the difference in the accuracy measuresbetween various prediction rules without requiring the correct specification of theproposed varying coefficient model. Simulation studies suggest that the proposedprocedures perform well in finite samples. We illustrate them here using a dataset ofpost-dialysis patients with end-stage renal disease.

Keywords: Survival Analysis, Risk Prediction, Varying Coefficient Model

AMS Classification: 97K80, 62N86

1Department of Biostatistics, Harvard School of Public [email protected]

2Dana-Farber Cancer Institute

3Department of Biostatistics, Harvard School of Public Health

78


About some old and new non-parametric controlcharts

Christian Paroissin1, Jean-Christophe Turlot2

SUMMARY

We are interested here in the design of non-parametric control charts which are pow-erful especially for positive random variables (say, for instance, lifetime distributions).We start by providing a short review of non-parametric control charts based on somefunctional of precedence statistics (this includes the Wilcoxon-Mann-Whitney statis-tic in particular) [1]. Then we propose some what seems to be a new functionalleading to a new control chart. The power of all these control charts is studied usingsimulation since computations are not always tractable.

Keywords: precedence statistic, Wilcoxon-Mann-Whitney statistic, numerical stud-ies

AMS Classification: 62G10, 62P30

References

[1] N. Balakrishnan & H.K.T. Ng (2006). Precedence-type tests and applications.Wiley, New-York.



79


Design of optimal progressively censored samplingplans using average risks

Carlos J. Perez-Gonzalez1, Arturo J. Fernandez2

SUMMARY

The optimal design of approximate reliability sampling plans is considered for progres-sively censored life tests when the lifetime variable follows a log-normal distribution.In the conventional acceptance sampling of a product is usually assumed a constantnonconforming proportion. However, in many cases, this proportion should not beconsidered constant. This paper presents a general procedure for determining theoptimal designs using average risks for a generalized beta family of priors. The use ofprior information to define the sampling risks can reduce, in many cases, the samplingsize of the designs despite the progressive censoring and provide a better assessmentof the true sampling risks. Several optimal sampling plans using this type of risks aretabulated for selected censoring levels and specifications according to the availablepartial prior information.

Keywords: reliability sampling plans, operating characteristic curve, acceptableand rejectable quality level, average producer’s and consumer’s risks

AMS Classification: 62N05

References

[1] ANSI/ASQC Z1.9 (1993) Sampling Procedures and Tables for Inspection byVariables for Percent Nonconforming, Milwaukee: American Society for Quality.

[2] Easterling, R. G. (1970) On the Use of Prior Distribution in Acceptance Sam-pling, Annals of Reliability and Maintainability, 5, 861–873.

[3] Hamada, M. S., Wilson A. G., Reese, C. S. y Martz, H. F. (2008) BayesianReliability, New York: Springer.

1Dept. of Statistics and Operations Research, University of La Laguna, [email protected]

2Dept. of Statistics and Operations Research, University of La Laguna, [email protected]

80


Modeling operational risk with Bayesian Extremevalue theory

Rivera Mancia Maria Elena1

SUMMARY

Modeling of operational risk has emerged as important risk component for financialand insurance institutions due to the severe losses that it has produced in the lastyears. One of the main problems in the study of operational risk is the availabilityof data since many operational losses are not recorded or simply because of theirlow frequency. However, some data sets have become available and have allowed toanalyze operational risk. In this study, an analysis of financial institutions internalloss data is performed using the Generalized Pareto Distribution by considering theuncertainty about the threshold. The proposed model considers the form of thedistribution below and above the threshold, combining a parametric estimation witha Bayesian approximation to perform inference about the unknown parameters inboth cases. The estimation is carried out using Markov Chain Monte Carlo (MCMC)methods, allowing posterior inference. After this, it is possible to determine theminimum capital requirements for operational risk.

Keywords: Operational Risk, Bayesian, Extremes

AMS Classification: 60G70, 62G32

1McGill University.Burnside Hall, Room 1023, 805 Sherbrooke Street West H3A 2K6,Montreal QC, [email protected]

81


Study of A-optimality for the univariate logisticmodel with random effects

M.T. Santos Martın1, J. M. Rodrıguez Dıaz2, C. Tommasi3

SUMMARY

Optimal designs for the logistic regression model have been extensively studied inthe context of fixed effects, but the interest in finding optimal designs for the modelwith random effects is steadily increasing (see for instance [1]). Recently [2] havestudied optimum designs for logistic models with random intercept. In this work A-optimal designs are derived for the univariate logistic regression model with normallydistributed random coefficients. An A-optimum design minimizes the average of thevariances of the optimal estimates for the parameters, and some integral approxima-tions are provided which are useful to compute numerically the designs.

Keywords: Logistic regression models, optimal design of experiment


References

[1] T. Holland-Letz, H. Dette and A. Pepelyshev (2011). A geometric char-acterization of optimal designs for regression models with correlated observations.Journal of the Royal Statistical Society B (in press).

[2] M. Ouwens, T. Frans and B. Martijn (2006). A maximin criterion for thelogistic random intercept models with covariates. J. Statist. Plann. Inference 136,926–981.

1Department of Statistics. University of [email protected]

2Department of Statistics. University of [email protected]

3Department of Economics, Business and Statistics.University of [email protected]

82


Comparing two approachesto the median of a random interval∗

Beatriz Sinova1, Ana Colubi1, Gerardo Sanz2

SUMMARY

Random intervals allow modelling situations in which the variable of interest is not areal one, but the range of values one experiment can take. This underlying imprecisionappears dealing with fluctuations, censored times or perceptions studied in manydifferent fields, like Biomedical or Social Sciences and Engineering. As it happenswith the mean in the real setting, the most usual central tendency measure (theAumann type expected value) is too influenced by the existence of ‘extreme’ data ordata changes. The idea of generalizing the concept of median because of its morerobust behaviour has been already developed by means of the L1 distance calledgeneralized Hausdorff metric. A different approach could be stated by using the δ1distance. The aim now is to compare the previous notion of median with the onebased on the δ1 distance by means of some simulation studies.

Keywords: random interval, median, δ1 distance, generalized Hausdorff metric

AMS Classification: 62G30, 62G35

1Departamento de Estadıstica e I.O. y D.M.,Universidad de Oviedo, 33071, Oviedo, [email protected], [email protected]

2Departamento de Metodos Estadısticos,Universidad de Zaragoza, 50009, Zaragoza, [email protected]

∗The research in this paper has been partially benefited from the Spanish Ministry of Scienceand Innovation Grants MTM2009-09440-C02-01 and MTM2010-15972. Beatriz Sinova has been alsogranted with an Ayuda del Programa de FPU (AP2009-1197) from the Spanish Ministry of Educationand an STSM from the COST Action IC0702.

83


Exit and ruin times for general renewal risk-models

Javier Villarroel1,

SUMMARY

When the classical Lundberg-Cramer model of risk theory is generalized to have arbi-trary i.i.d. holding times (cf. [1],[2]) those results derived at jump times will not carryover to arbitrary present due to the lack of Markoviannes. In particular exit timesdepend on the actual state and available information. Here we consider mean ruintimes assuming that the present is not necessarily a jump instant, and also a partialknowledge from the observer. We show how the solution to this problem involves ideasdrawn from renewal theory. It is found that key properties of a companion integralequation depend on the relative sign of drift and jumps. If this ratio is positive thesolution can be given in closed form. For the opposite-sign case we analyze a familyof solvable cases. The results may be relevant to predict the mean time for an in-surance company to go bankrupt when the information regarding the company’s pastperformance has not been disclosed and only the actual company budget is available.

Keywords: risk theory, mean ruin times

AMS Classification: 91B30, 60K15, 60J75

References

[1] S. Li and J. Garrido(2004). On ruin for the Erlang(n) risk process. Insur. Math.Econ. volume(34), 391-408.

[2] D. C. M. Dickson (1998). On a class of renewal risk process. North Am. Act.J. volume(2), 60-68.

1Universidad de Salamanca, Fac. de Ciencias, 37008 Pza Merced s/[email protected]

84


Ageing properties of some bivariate distributionsfrom the Farlie-Gumbel-Morgenstern family∗

Juana-Marıa Vivo1, Manuel Franco2

SUMMARY

In many practical problems, bivariate lifetime data frequently arise, it is of great in-terest to consider different bivariate distributions and their ageing properties are alsouseful, as it is often important to make explicit assumptions on the underlying dis-tribution. The lifetime of one system is determined by its components and structure.For instance, in reliability and biological systems the components or organ lifetimesare often positively dependent in some stochastic sense. The most of the systemsformed in the real life are the series and parallel systems, which are determined bythe working of all or at least one of these components, respectively. Thus, the age-ing properties of its series and parallel systems formed with components having suchbivariate distributions also become of interest in such applications.

In the literature, different procedures have been used to generate bivariate distri-butions (cf. [1], among others). For example, some distributions of Marshall-Olkintype have been recently analyzed (cf. [2], [3]). Another well-known procedure is theFarlie-Gumbel-Morgenstern system, having a simple natural dependent structure withgiven marginals. In this work, we study some ageing properties of specific bivariatedistributions belonging to the Farlie-Gumbel-Morgenstern class of distributions.

Keywords: Ageing, series and parallel systems, Farlie-Gumbel-Morgenstern family

AMS Classification: 62H10, 62N05, 91B02

References

[1] Balakrishnan, N., Lai, C.D. (2009). Continuous Bivariate Distributions, 2nd ed.Springer, New York.

[2] Kundu, D., Gupta, R.D. (2010). Modified Sarhan-Balakrishnan singular bivariate dis-tribution. J. Statist. Plann. Infer., 140, 526-538.

[3] Sarhan, A.M., Balakrishnan, N. (2007). A new class of bivariate distributions andits mixture. J. Multivariate Anal. 98, 1508–1527.

1Department of Quantitative Methods for Economy, University of [email protected]

2Department of Statistics and Operations Research, University of [email protected]

∗This work was partially supported by Fundacion Seneca of the Regional Government of Murcia(Spain) under Grant 11886/PHCS/09.

85


Song’s measure of the shape and its application todetect departure from a specific elliptic distribution

Konstantinos Zografos1, Apostolos Batsidis2

SUMMARY

The aim of this talk is twofold. On the one hand to present a measure of the shapeof a probability distribution and to study its performance in the elliptic family ofprobability distributions. On the other hand to introduce and study a necessarytest for detecting departures from specific elliptic distributions, based on the sampleversion of Song’s measure of the shape. In respect to the first purpose, informationtheoretic quantities based on Shannon or Renyi entropies and the mutual informationprovide with nice descriptive measures of a probability distribution. Among them, ameasure introduced by Song (2001) on the basis of Renyi entropy, may be used as adescriptive measure of the shape. In the first part of the talk, Song’s measure will beapplied, studied and compared, with other measures, in the broad class of the ellipticdistributions. In the second part of this talk, the empirical version of Song’s measure,introduced by Zografos (2008), will be exploited in order to present a necessary testfor testing whether a data set is coming from a specific elliptic distribution. Theperformance of the test is evaluated by means of a simulation study which controlstype I error and power.

Keywords: Shannon-Renyi entropy, Song measure, kurtosis, elliptic distributions.

AMS Classification: 62H05, 62E10, 62H15

References

[1] Song, K.-S. (2001). Renyi information, loglikelihood and an intrinsic distributionmeasure. J. Statist. Plann. Inference 93, 51–69.

[2] Zografos, K. (2008). On Mardia’s and Song’s measures of kurtosis in ellipticaldistributions. J. Multivariate Anal. 99, 858–879.

1University of Ioannina, Department of Mathematics, 451 10 Ioannina, [email protected]

2University of Ioannina, Department of Mathematics, 451 10 Ioannina, [email protected]

86


A Bayesian approach to bandwidth selection inunivariate associate kernel estimation

N. Zougab1, S. Adjabi2, C.C. Kokonendji2

SUMMARY

The fundamental problem in the associate kernel estimation of density or probabil-ity mass function (pmf) is the choice of the bandwidth. In this paper, we use aBayesian approach based upon likelihood cross-validation and Monte Carlo MarkovChain (MCMC) method for deriving the global optimal bandwidth. A comparativesimulation study of the MCMC method and the classical methods which adopt theasymptotic mean integrated square error (AMISE) as criterion and the cross valida-tion is presented for data generated from known densities and pmf, using standardAMISE and the practical integrated squared error. The simulation results show thesuperiority of the MCMC method over the classical methods.

Keywords: Cross validation, Associate kernel estimation, Likelihood, MCMC method.

AMS Classification: 62G07, 62E15.

References

[1] A. Gelman and J B. Carlin and H S. Stern and D B. Rubin (1995).Bayesian Data Analysis. Chapman and Hall, London.

[2] C C. Kokonendji and T. Senga Kiesse and S S. Zocchi (2007). Discretetriangular distributions and non-parametric estimation for probability mass func-tion. Journal of Nonparametric Statistics volume(19), 540–547.

[3] S J. Sheather and M C. Jones (1991). A reliable data-based bandwidth selec-tion method for kernel density estimation. Journal of the Royal Statistical SocietySeries B volume(53), 683–690.

[4] B W. Silverman (1986). Density Estimation for Statistics and Data Analysis.Chapman and Hall, New York.

[email protected]

87

INDEX OF

AUTHORS

Index

Abaurrea, Jesus, 35, 36Adjabi, S., 87Afere, B.A., 37Al-Awadhi, Fahimah, 66Alcaide, David, 38Alonso, Maria Pilar, 39Amaya, Jorge, 40Amo-Salas, Mariano, 41Asın, Jesus, 35, 36Avram, Florin, 42

Balakrishnan, Narayanaswamy, 29Basu, Ayanendranath, 43Batsidis, Apostolos , 86Beamonte, Asuncion, 39Bobecka, Konstancja, 44Bordes, Laurent, 45Borque, Angel, 56Braekers, Roel, 46

Cai, Tianxi, 78Casanova, Jose, 47Casero-Alonso, Vıctor, 48Cebrian, Ana Carmen, 35, 36Cheng, Su-Chun, 78Collet, Francesca, 49Colubi, Ana, 83Combarro, E.F., 73Coolen-Maturi, Tahani, 50

Dıaz, 73Das, Debabrata, 51de la Rosa de Saa, Sara, 52Doostparast, M., 53Dutta, Pankaj, 51

Ekhosueh, Virtue U., 54Ersel, Derya, 55Esteban, Luis Mariano, 56

Fernandez-Guerrero, Mercedes, 57Fernandez-Ponce, J.M., 58Fernandez, Arturo J., 80

Franco, Manuel, 85

Gaddah, Auguste, 46Galbete, Arkaitz, 59Garcıa-Laguna, Juan, 77Gargallo, Pilar, 39Gavın, Natalia, 36Gil, Marıa Angeles, 31Gonzalez Sierra, Miguel Angel, 38Gouet, Raul, 60–62Gutierrez Pena, Antonio, 76Gutierrez, R., 75Gutierrez-Sanchez, R., 75

Hadi, Ali S., 32, 63Hitczenko, Pawe l, 44

Ishiekwene, Cyril Chukwuka, 64

Jodra, Pedro, 65

Kojadinovic, Ivan, 45Kokonendji, C.C., 87Konsowa, Mokhtar, 66Koyuncu, Nursel, 67

Lopez-Blazquez, Fernando, 44, 70Lopez-Fidalgo, Jesus, 30, 41, 48Lopez, F. Javier, 60–62Lopez, Marıa Teresa, 52Lacruz, Beatriz, 47, 63, 68Lahoz, David, 68Leisen, Fabrizio, 49, 69Leonenko, Nikolai, 42Lijoi, Antonio, 49Lubiano, Marıa Asuncion, 52

Maldonado, Lina P., 60Malina, Magdalena, 71Mandal, Abhijit, 43Martın-Martın, Raul, 57Martin, Nirian, 43, 72Mata, Raquel, 72

90

INDEX OF AUTHORS SPO 2011 Jaca, September 13–16th 2011

Mateo, Pedro M., 68Miranda, P., 73Moler, Jose Antonio, 59Molina, Manuel, 74Mota, Manuel, 74Moustafa, Rida E., 32

Nafidi, A., 75Nunez Antonio, Gabriel, 76

Ortiz, Jesus M., 47Osagiede, Augustine A., 54Oyegue, F.O., 37

Perez-Gonzalez, Carlos J., 80Palacios-Rodrıguez, F., 58Pando, Valentın, 77Parast, Layla, 78Pardo, Leandro, 43, 72Paroissin, Christian, 79Perez-Palomares, Ana, 63Plo, Fernando, 59

Ramırez, Hector, 40Ramos, Alfonso, 74Ramos, E., 75Rempa la, Grzegorz, 44Rivera Mancia Maria Elena, 81Rodrıguez-Aragon, Licesio J., 57Rodrıguez Dıaz, J.M., 82Rodrıguez-Grinolo, R., 58

Salamanca-Mino, Begona, 70Salvador, Manuel, 39San-Jose, Luis A., 77Santos Martın, M.T., 82Sanz, Gerardo, 56, 60–62, 83Sicilia, Joaquın, 38, 77Sinova, Beatriz, 83Suleyman, Gunay, 55Suvak, Nenad, 42Symanzik, Jurgen, 32

Tommasi, C., 82Turlot, Jean-Christophe, 79

Uribe, Paula, 40

Vandekerkhove, Pierre, 45Velayati Moghaddam, E., 53Villarroel, Javier, 84Vivo,Juana-Marıa, 85

Weso lowski, Jacek, 44

Zografos, Konstantinos, 86Zougab, N., 87

91

LIST OF

PARTICIPANTS

SPO 2011 Jaca, September 13–16th 2011 LIST OF PARTICIPANTS

Abaurrea, [email protected]

Afere, Benson [email protected]

Ajagbe, Olakunle [email protected]

Ahmed, [email protected]

Alberto, [email protected]

Alcaide, [email protected]

Alvarez, [email protected]

Amaya, [email protected]

Amo, [email protected]

Asın, [email protected]

Avram, [email protected]

Babatunde, Olusola [email protected]

Balakrishnan, [email protected]

Beamonte, Marıa [email protected]

Bernardoff, [email protected]

Bobecka, [email protected]

Bordes, [email protected]

Braekers, [email protected]

Casero , Victor [email protected]

Cebrian, Ana [email protected]

Collet, [email protected]

Das, [email protected]

de la Rosa de Sa, [email protected]

Doostparast, [email protected]

Ekhosuehi, Virtue [email protected]

Ersel, [email protected]

Esteban, Luis [email protected]

Galbete, [email protected]

Gargallo, [email protected]

Gavın, Nataliags [email protected]

94

LIST OF PARTICIPANTS SPO 2011 Jaca, September 13–16th 2011

Gil, Marıa [email protected]

Hadi, Ali [email protected]

Ishiekwene, Cyril [email protected]

Jodra Esteban, [email protected]

Konsowa, [email protected]

Koyuncu, [email protected]

Lacruz, [email protected]

Lahoz, [email protected]

Leisen, [email protected]

Lopez, F. [email protected]

Lopez-Fidalgo, [email protected]

Lopez-Blazquez, [email protected]

Maldonado, [email protected]

Malina, [email protected]

Mallor, Fermı[email protected]

Martın, [email protected]

Mata, [email protected]

Mateo, [email protected]

Maturi, [email protected]

Miranda, [email protected]

Moler, Jose [email protected]

Molina, [email protected]

Nunez, [email protected]

Odiase, Justice [email protected]

Osagiede, Augustine [email protected]

Palacios, [email protected]

Parast, [email protected]

Pardo, [email protected]

Paroissin, [email protected]

Perez Gonzalez, [email protected]

95

SPO 2011 Jaca, September 13–16th 2011 LIST OF PARTICIPANTS

Perez-Palomares, [email protected]

Plo, [email protected]

Reyes, [email protected]

Rivera, Marıa [email protected]

Rodrıguez, Licesio [email protected]

Rodrıguez, Juan [email protected]

Salvador, [email protected]

Santos, M. [email protected]

Sanz, [email protected]

Sicilia, Joaquı[email protected]

Sinova, Beatrı[email protected]

Turlot, [email protected]

Villarroel, [email protected]

Vivo, Juana-Marı[email protected]

Vysotsky, [email protected]

Wesolowski, [email protected]

Zografos, [email protected]

96

Documents

PROGRAM & ABSTRACTS - Universidad de Zaragozametodosestadisticos.unizar.es/~jaca2011/Program.pdf · PROGRAM & ABSTRACTS. ... Sara de la Rosa de S aa, ... Analysis of Demographic and