Andreas Karlsson

Statistical Matching: Theory and Practice

and relevant numerical linear algebra. R is available at cran.r-project.org as are the R package used in this book, mgcv, and the datasets, gamair. The book comprises six chapters. Chapters 1 and 2 provide an elegant and remarkably complete summary of inference on linear models and generalized linear models. It starts by asking the question “How old is the universe?,” using the measurements from the Hubble Space Telescope key project to study the relationship between distance and velocity for 24 galaxies containing Cepheid stars. Chapter 3 introduces the framework of GAMs, Chapter 4 provides details of the theory and methods of using them, and Chapter 5 illustrates the practical use of GAMs using the R package mgcv. Chapter 6 looks at mixed model extensions of linear, generalized linear, and generalized additive models. This chapter shows how the smooth functions can be absorbed into the mixed model framework by decomposing them to fixed effects and random effects components. Experienced researchers in this area may find the book by Hastie and Tibshirani (1990) somewhat more technical in nature. The monographs by Wahba (1990) and Gu (2002) are cited extensively for their theoretical work on the spline basis. There are also a number of other packages implementing GAMs and related models for R. For example, Trevor Hastie’s gam package, which is a port to R of the original gam in S–PLUS, and Chong Gu’s gss package, which is a complete package for general smoothing spline models. Nevertheless, Generalized Additive Models: An Introduction With R presents a neatly focused account of GAMs theory and practical application. It is written with attention to style and clarity and produced to help the reader grasp the concept as easily as possible. This book is a valuable addition for learning about GAMs not only for researchers and practitioners, but also for students in the classroom. The preface helps the reader to find his/her own way to work through the book.

Matrix Analysis for Statistics

This is a research monograph rather than a practical book or, even less, a textbook. For the latter, your needs are better served by Ramsay and Silverman (2005a, b). In a sense, the present book is heavily biased toward statistical theory and is weak on practice and applications. For the theory aspect, the present book does bring something new and, indeed, some novel theoretical investigations into the kinds of functional data problems not addressed by Ramsay and Silverman (2005a). While Ramsay and Silverman’s books focus on exploratory and data analytic techniques for sparsely observed functional data, and employ techniques for smoothing and extrapolation using smoothing spline methods, the present book focuses on issues that arise from analysis of high resolution functional data, which can be easily registered or made to balance (pp. 33–34). The present book applies kernel regression techniques to functional data problems such as functional regression or classification, where the predictor is a function. The use of “nonparametric” in the title, although appropriate, is not totally distinctive, because I consider most techniques used in Ramsay and Silverman (2005a) nonparametric as well. The book mentions several applications in chemometrics, speech recognition, and electricity consumption forecast. I would like to add more, such as climate data analysis, material sciences, and bioinformatics. As someone who works closely with scientists on various interdisciplinary investigations on a daily basis, I feel strongly that there is need for new statistics that can deal with increasingly high throughput and high resolution measurements. Modern data analysis can benefit greatly from the recent statistical advent in functional data analysis. I think there will be many developments in the area of high-dimensional statistics when there are more observed variables than the number of replicates or samples, and multivariate statistics should receive revived interest in statistical research. In a sense, rather than sticking strictly with the existing techniques, one should adopt a pioneering attitude toward functional data analysis, and professional statisticians should be prepared to develop on their own techniques appropriate for a given problem, because much new statistics remains to be developed for the emerging problems (Lu 2006). Nonparametric statisticians should feel very much at home with the approach taken in this book. The authors have defined a broad and interesting framework in Part I, such as functional statistics, semimetrics, and locally weighted regression for functional data. Theoretical results, mainly asymptotics, are provided in Part II. Part V also contains some relevant theory and should be read right after Part II. I should point out some very relevant early work on nonparametric regression with fractal design (Lu 1999). Part III of the book deals with classification problems of functional data. Part IV is unusual, in that it deals with time series and dependent data. Although time series is among my favorite subject, it does not appear obvious how this part fits into the functional data framework, although one may argue that for high frequency time series, functional statistics may be very relevant. Notwithstanding, I do think the present book is a worthy contribution to the literature. The authors have done a nice job of summarizing some of ongoing research, on which some of the papers exist only in proceedings or in the French literature. Researchers in the growing functional statistics community should be glad to have a copy of the book.

Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series

This book is a step-by-step guide written primarily for executives and managerial professionals involved in the design and analysis of clinical experiments. The book is based on the well-known industrial formula of planning, implementation, and carrying out checks. Chapter 2 provides a set of guidelines for the successful design and conduct of clinical trials which includes a brief discussion of starting a project with report review, using the computer to store all information, working with regulatory agencies, and the importance of keeping things simple, to name a few. Chapter 3 provides an outline of key steps in designing and conducting clinical trials. Chapter 4 discusses the starting needs for the project, and Chapter 5 provides a predesign checklist. Technical design considerations, including statistical experimental design, are covered in Chapter 6. This chapter briefly discusses the concepts of controlling, blocking, and randomizing. The issue of sample size is also mentioned, as well as a few statistical definitions, such as type I and type II error probabilities. Chapter 7 covers exception handing. Chapter 8 describes documentation needs of clinical trials. Chapter 9 provides a discussion of things to consider when recruiting patients and physicians. Chapters 10 and 11 discuss about how to use computers to manage data. Chapter 12 provides a master checklist for someone who is about to start a project. Chapters 13 and 14 discuss how to monitor and manage trials, and the final chapter goes over a few issues in data analysis for clinical trials. Design and analysis of clinical trials is a statistical subject, but this book glosses over the statistical issues. A reader looking for technical details about statistical issues involved in clinical trials would do better to turn one of many excellent books available on this topic (see, e.g., Fleiss 1986; Everitt 2004; Chow and Liu 2004). If you are looking for a technical book on the subject, then this is not the book for you. However, if you are interested in gaining general information about clinical trials, then you will find this book very useful.

Estimation in Surveys with Nonresponse

The editors–authors have collected 16 chapters by 34 leading experts on the mathematical theory of stochastic optimization methods with potential for application to the engineering design of complex systems (e.g., telecom and computer networks and aircraft control systems). Make no mistake, however, this is not an applied text. The emphasis of this book is mathematical theory, and the presentation is highly mathematical and intended for an audience of researchers in the fields of control and optimization. The level of mathematical sophistication is typical of a Journal of the American Statistical Association article, and nearly all chapters are article length and similar in structure: problem introduction, theorems and proofs, examples, and conclusions. This book probably will appeal only to those Technometrics readers who have a control systems or operations research background. Also, if you derive your inspiration primarily from application examples, they are in limited supply here. In the Preface, the editors state that their objective is to discover engineering design parameter settings that produce the most robust (insensitive) system response to process disturbances or loads when the magnitude and description of the disturbances is uncertain. Their subject is the mathematical theory common to control systems and generic decision optimization problems with inexact design data. Their strategy is to bring together researchers from the fields of optimization and control with the intentions of highlighting the opportunities for synergistic interaction between the two fields, and focusing on randomized and probabilistic techniques for solving engineering design problems in the presence of stochastic uncertainty. The result is a mathematical “tour-de-force” of the current state of research in the mathematics of optimization problems in which chance plays a substantial role. Chance may enter these problem formulations through probabilistic constraints or stochastic solution methods (Part I, Chaps. 1–4), the search for robust design outcomes via randomization and sampling methods (Part II, Chaps. 5–9), or the use of probabilistic methods of system identification (fitting time series) and control (Part III, Chaps. 10–16). Chapters 1–4 cover scenario approximations of chance constraints, optimization models with probabilistic constraints, a theoretical framework for comparing several stochastic optimization approaches, and the optimization of risk measures. Chapters 5–9 explore sampled convex programs and probabilistically robust design, randomized constraint sampling applied to the game Tetris, near optimal solutions to least squares problems with stochastic uncertainty, the randomized ellipsoid algorithm for constrained robust least squares problems, and randomized algorithms for semiinfinite programming problems. Chapters 10–16 discuss a learning theory approach to system identification and stochastic adaptive control, probabilistic design of a robust controller using a parameter dependent Lyapunov function, probabilistic robust controller design using the probable near minimax value and randomized algorithms, sampling random transfer functions, nonlinear systems stability via random and quasi-random methods, probabilistic control of nonlinear uncertain systems, and fast randomized algorithms for probabilistic robustness analysis. The writing styles are generally quite readable, although the dense mathematical symbolism varies between chapters and is not generally defined in chapter glossaries. The common reference list is extensive (411 entries!). The index is a scant 2 pages. Graphics are limited (21 figures), but useful. English usage is uniformly good and the editors have made it understandable to a mathematically sophisticated audience. Although only Chapters 13–15 discuss detailed examples, the range of application areas cited throughout include matching cash flows to demands, truss topology, robust antenna array design, portfolio optimization, robust estimation, control system analysis and synthesis, hard stochastic control, interpolation of interval data, Affine uncertainty, Kalman filter design for uncertain systems, optimal and robust control, optimal experimental design, system reliability, system identification (fitting time series), stability of a tower crane, aircraft lateral motion control, multidisk control problem, linear time-invariant plant transfer functions, mobile robot stability, and hypersonic aircraft control models. I found Chapter 3, by Spall, Hill, and Stark, to be quite useful and the exception to the style of the other chapters with minimal use of symbolism. Their comparison of optimization approaches complements the book by Spall (2003) on stochastic optimization, reviewed by Hesterberg (2004). Chapter 7, by the editors, was quite approachable because of the more typical algebraic development, numerical examples, and graphics. Their discussion of the learning theory approach to stochastic uncertain least squares problems was straightforward and informative. Chapter 15, by Wang and Stengel, on hypersonic aircraft control models was interesting and informative, perhaps because of the examples. The remaining chapters are sufficiently abstract to appeal primarily to researchers and subject matter experts. It appears that the editors have succeeded in their intention, although it was certainly eye-opening to see the current state of research in stochastic optimization theory. The individual chapter authors have contributed a vast reference list that alone is worth the price.

Elementary Survey Sampling

Empirical evidence to lend proper credence, however, continues to elude the quality literature. This hardly vexes Taguchi (or most of those who produce the corpus of the discipline), but it is importunate to the reviewer. In many settings, the loss function is unlikely to be symmetric with respect to the target and, furthermore, the behavior on either side of the target is not necessarily the same. Such seemingly obvious deviations have not deterred the vast majority from proclaiming the ubiquity of the function. The current book offers no new insights here. The treatment of experimental design is fairly strong. Taguchi’s use of outer arrays is one of his greatest contributions (and one that has caught the ire of a few academics). The book elucidates design adequately and illuminates Taguchi’s advances. Anyone who is well versed in design will be able to skip the introductions and go straight to the discussion of orthogonal arrays. In this reviewer’s opinion, this is the major strength of the book. Another strength is the extensive set of case studies that cover each topic from the previous chapters. Applications include robust engineering in polymer chemistry, material design in automatic transmissions, improvements in omelet taste, and the use of Mahalanobis distance to measure drug efficacy. The sheer range of topical coverage in the cases will doubtlessly find appeal for virtually any practitioner regardless of specific field. There is the obligatory mention of Six Sigma as it relates to Taguchi’s work. Given the scope of Six Sigma in the current landscape, finding your place therein is necessary. A glaring omission is the lack of a similar consideration of ISO and QS certifications (as is given in Juran). Do not assume that the reviewer sees this as a negative. It is hoped here that Taguchi sees these quality certifications as largely specious and unworthy of a reference. Overall, it is hard not to be impressed with the utter volume of Taguchi’s output. The expanse of coverage is not to be dismissed. As a vehicle for presenting his prolific production, the handbook succeeds. The book may appear to be somewhat self-indulgent (as if 1600+ pages about your previous work could appear otherwise!). No doubt an ambitious undertaking, the authors nevertheless generally hit their mark. One would be hard-pressed not to at least enjoy most of the ride. What is positive (negative) about the book is largely what one perceives to be positive (negative) about Taguchi. The aforementioned lack of scholarly references is unsurprising, because Taguchi largely practiced beyond the boundaries of academia. Many academics have tended to reciprocate with less attention to his work than is probably deserved. What can safely be said is that if you are a fan of Taguchi’s work, this is definitely for you. If you need a single reference for his work or simply desire a “complete quality library,” you cannot go wrong here. Otherwise, it is unlikely that you would be interested. But in the event that you are a practitioner itching to get acquainted with Taguchi and have

Precedence-Type Tests and Applications

150 burning a hole in your wallet or Visa, this one’s a winner.

Statistical Matching: Theory and Practice:Statistical Matching: Theory and Practice

Bobman, S., Riederer, S., Lee, J., Suddarth, S., Wang, H., and MacFall, J. (1985), “Synthesized MR Images: Comparison With Acquired Images,” Radiology, 155, 731–738. Bobman, S., Riederer, S., Lee, J., Tasciyan, T., Farzaneh, F., and Wang, H. (1986), “Pulse Sequence Extrapolation With MR Image Synthesis,” Radiology, 159, 253–258. Glad, I., and Sebastiani, G. (1995), “A Bayesian Approach to Synthetic Magnetic Resonance Imaging,” Biometrika, 82, 237–250. Hyvärinen, A., Karhunen, J., and Oja, E. (2001), Independent Component Analysis, New York: Wiley. Maitra, R., and Besag, J. E. (1998), “Bayesian Reconstruction in Synthetic Magnetic Resonance Imaging,” in Bayesian Inference in Inverse Problems. Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE 1998) Meetings, Vol. 3459, ed. A. Mohammad-Djafari, pp. 39–47. R Development Core Team (2006), “R: A Language and Environment for Statistical Computing,” in R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0, available at http://www.R-project.org.