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This article was downloaded by: [Case Western Reserve University] On: 31 October 2014, At: 10:43 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Journal of the American Statistical Association Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uasa20 Functional Approach to Optimal Experimental Design Christine M Anderson-Cook a a Los Alamos National Laboratory Published online: 01 Jan 2012. To cite this article: Christine M Anderson-Cook (2007) Functional Approach to Optimal Experimental Design, Journal of the American Statistical Association, 102:477, 386-386, DOI: 10.1198/jasa.2007.s174 To link to this article: http://dx.doi.org/10.1198/jasa.2007.s174 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

Functional Approach to Optimal Experimental Design

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This article was downloaded by: [Case Western Reserve University]On: 31 October 2014, At: 10:43Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Journal of the American Statistical AssociationPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/uasa20

Functional Approach to Optimal Experimental DesignChristine M Anderson-Cooka

a Los Alamos National LaboratoryPublished online: 01 Jan 2012.

To cite this article: Christine M Anderson-Cook (2007) Functional Approach to Optimal Experimental Design, Journal ofthe American Statistical Association, 102:477, 386-386, DOI: 10.1198/jasa.2007.s174

To link to this article: http://dx.doi.org/10.1198/jasa.2007.s174

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose ofthe Content. Any opinions and views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be reliedupon and should be independently verified with primary sources of information. Taylor and Francis shallnot be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and otherliabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to orarising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Functional Approach to Optimal Experimental Design

386 Book Reviews

Diagnostics are revisited, and Bartlett’s test is presented in detail. Finally, in-troductions are provided to logistic regression, M-estimation, and total leastsquares.

A major feature of this book is the inclusion of optional linear algebra sec-tions and problem sets, which are given for all but one of the chapters. In addi-tion, there is a 16-page appendix that can provide a refresher or as an introduc-tion to linear algebra. The goal of these sections is to demonstrate the powerand flexibility of the linear algebra approach to linear models. Initially, this ma-terial is mechanical in nature. In later chapters (Chap. 7 and beyond), the scope,depth, and volume of the linear algebra sections and exercises increases sharply.This later material will be beyond the reach of the student without a prior lin-ear algebra course, but will be a boon to the initiated undergraduate or possiblyto the nonmajor graduate student. The linear algebra sections are fairly briefand do not attempt to recapitulate the entire chapter, but rather highlight twoor three ideas previously introduced. These discussions advance to the pointof introducing orthogonal projection operators and subspaces. A version of theGauss–Markov theorem is subsequently presented and proven. Most argumentsare coordinatized, and a full-rank design matrix is assumed.

The problem sets are particularly strong. There are, of course, many data-oriented exercises that allow the student to work with the methods discussed.These problems are rarely purely mechanical and often ask the student to thinkabout the analysis while proceeding. Each chapter also has several theoreticalor mathematical exercises, which typically are very good. These problems of-ten significantly expand the scope in the sense that they introduce new ideasand techniques. Occasionally students are asked to produce simulation-basedsolutions to problems. The exercises are characterized by both diversity andbreadth. Although the authors promise to indicate which problems require cal-culus, which require simulation, and which require “just a little more persis-tence,” they do not seem to follow this practice religiously. For example, prob-lems in the latter category are indicated only in the first two chapters.

My criticisms of the text are minor. Given the vast nature of the topic area,the authors certainly needed to make some tough decisions regarding coverage.Having said that, I note that the discussions focus on regression models (quan-titative covariates). The last chapter does discuss some one-way ANOVA andANCOVA models, but goes no further. There is no discussion of two-way orhigher models, or of experimental design models. These are models that theintended audience will encounter sooner rather than later. In addition, somemay feel that the chapter on inference should be a bit broader. Unbiasednessis the only estimation criterion discussed carefully, and the introductions toconfidence intervals and testing are done almost exclusively through examples.Testing is often a troublesome area for students, and the authors seem to breaktheir own rule here regarding the provision of mathematical background. Myreview revealed a number of typographical and other errors commensurate witha first edition.

In summary, Introduction to Linear Models and Statistical Inference re-flects a strong appreciation of both theory and the realities of practical modelbuilding. The book is intended for a broad audience, and the availability of anelectronic version should widen its appeal by expanding its accessibility. Theauthors’ many years of teaching experience are evident, and the beginning orintermediate statistics student should come away with an understanding that an-alyzing real data requires thoughtfulness and completeness. Truly linking meth-ods and theory in an area like linear models is not trivial for most students, buttools like this one go a long way toward bridging that gap.

Lane A. EUBANK

Pharmacyclics, Inc.

Functional Approach to Optimal Experimental Design.

Viatcheslav B. MELAS. New York: Springer, 2006. ISBN 0-387-98741-X.ix + 333 pp. $59.95 (P).

Optimally designed experiments for a wide class of linear and nonlinear re-gression models are actively studied in the statistical community. This bookcontains a comprehensive and cohesive presentation of the author’s publishedwork in this area since 1995. The book summarizes previous work and unifiesresults obtained by constructing optimal designs for polynomial, trigonometri-cal, rational, and exponential models.

Chapters 1 and 2 provide an overview of optimal experimental design, out-lining many of the key theoretical results underlying the work. Also included

are the definitions of the many optimality criteria considered (D-, G-, MV-, c-,and E-) along with an overview of the functional approach.

The remaining chapters focus on various combinations of model types andoptimality criteria. The material presented is at a sophisticated mathematicallevel, with a strong emphasis on the construction of various designs, ratherthan a connection to why these strategies create designs that are desirable forpractical implementation. The unified approach helps consolidate the individ-ual pieces that the author has published previously, and provides greater insightsinto the applicability of the methods.

Christine M. ANDERSON-COOK

Los Alamos National Laboratory

Statistical Matching: A Frequentist Theory, Practical Applicationsand Alternative Bayesian Approaches.

Susanne RÄSSLER. New York: Springer, 2002. ISBN 0-387-95516-X.xviii + 238 pp. $79.95 (P).

Statistical matching, as construed by the author, deals with extracting moreinformation from multiple related datasets than may seem to be present.To understand the issues, consider two databases, one consisting of vectors(Xi1, . . . ,Xik,Zi1, . . . ,Zim) for subjects i = 1, . . . ,P and the other of vectors(Zj1, . . . ,Zjm,Yj1, . . . , Yj�) for subjects j = 1, . . . ,Q. For instance, Z maycontain household demographics, X health information, and Y economic infor-mation. Of course, the relationship between economic and health informationmay be of interest for policy or research purposes, even though neither databasecontains both.

The fundamental question is how to extract such information and character-ize resultant uncertainties when the overlap between the sets of subjects is notknown or cannot be determined. In the extreme case, the two databases have nosubjects in common, which is the diametric opposite of record linkage (Fellegiand Sunter 1969), where the sets of subjects are identical but the Z-attributesthat are common to both databases are not primary keys. Calling this a missingdata problem, although accurate, is not entirely useful. “Missing-at-random”assumptions are not valid. Imputation, or even multiple imputation, may intro-duce large model-based uncertainties. The unknown nature of the dependencebetween the two databases must be taken into account. (Surely the cases whereboth databases come from New York City and where one is from Chapel Hill,NC and the other from North Dakota differ.)

This book articulates a theoretical framework that allows these kinds ofquestions to be posed meaningfully. It is derived from the author’s habilita-tion thesis. Not surprisingly, the powerful approaches are Bayesian, with rootsin the work of Rubin (1986, 1987), but there is discussion of frequentist theo-ries as well. Examples are based on both real and simulated data. S–PLUS codeis included, although it is not clear that either the techniques or the particularalgorithms scale to really large databases.

There are a couple of unfortunate omissions. First, the book focuses (albeitnot exclusively) on numerical data, whereas many important official statisticsdatabases contain partially or primarily categorical variables. Second, the prob-lem has important cost implications—conducting an additional survey that asksboth economic and health questions may not be an affordable option—but theseare not treated in the book. It is important to understand that both cost and dataquality considerations prohibit extracting as much information as possible fromexisting data.

Had Springer-Verlag priced this paperback book of fewer than 250 pagesat a more modest level, it would have reached a broader audience. Those seri-ously interested in official statistics and missing data should consider buying itnotwithstanding the price.

Alan F. KARR

National Institute of Statistical Sciences

REFERENCES

Fellegi, I. P., and Sunter, A. B. (1969), “A Theory for Record Linkage,” Journalof the American Statistical Association, 64, 1183–1210.

Rubin, D. B. (1986), “Statistical Matching Using File Concatenation With Ad-justed Weights and Multiple Imputations,” Journal of Business & EconomicStatistics, 4, 87–94.

(1987), Multiple Imputation for Non-Response in Surveys, New York:Wiley.

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