C 2006) pp. 1074–1075 Annals of Biomedical Engineering, Vol. 34, No. 6, June 2006 (
DOI: 10.1007/s10439-006-9109-5

Book Review some alternative methods of resampling and summarizing the chapter. Working with small sample sizes does have its practical limitations, which need to be considered when applying bootstrap techniques. For example, the authors state: “Of course the original sample has to be a good representation of the population and it should not include too many outliers.” (p. 20). While this is good advice, and one of the assumptions for bootstrap, practically one would not know if a small sample is indeed a “good representation” of the population, or the percentage of outliers in one’s sample. When discussing the principle of moving block bootstrap (resampling of dependent data), the authors suggest: “we randomly select blocks of length l from the original data and concatenate them together to form a resample . . .” (p. 29). No criterion is given for selecting the block size. The authors do not mention that if ill chosen, one would lose waveform information embedded in the original data. Correctly choosing block lengths would depend on knowing a priori the waveform’s period. When discussing the limitations of bootstrap techniques, the authors provide examples of these failures, but do not adequately explain why these techniques fail, or what can be done (from a practical perspective) to either recognize these failures, or guard from them occurring in the first place. This is in part because optimal bootstrap parameters are dependent on the particulars of the application, and are determined by the practitioner’s experience and through trial and error. Chapter 3 focuses on hypothesis testing, pivoting (and its limitations), estimating variance (including jackknife techniques), regression, and the matched filter. Throughout the chapter, examples are provided to illustrate the technique under discussion. Computational cost considerations are woven into the discussion. However, with the profusion of computers in the workplace, computational costs are relevant only in real-time situations (like radar applications, which are the primary applications discussed in this chapter). Chapters 2 and 3 are the most useful in equipping most practitioners with the necessary tools for applying bootstrap techniques to real-world applications. Chapter 4 focuses on model selection and defines two broad classes of models. The first type are “statistical models” (ie predictive models) such as linear and non-linear models that describe the physical environment. The second type are “data models” that are generic descriptions of the data (such as autoregressive models). These models are use-

(Published online: 5 May 2006)

Bootstrap Techniques for Signal Processing. By Abdelhak Zoubir and Robert Iskander, Cambridge University Press, 217 pp. ISBN 0-521-83127-X, Hardcover $75 Bootstrap techniques are among the most powerful techniques used today to draw inferences from small data sets. Bootstrap Techniques for Signal Processing focuses on introducing bootstrap techniques from primarily an applications perspective (ie the mechanics of applying this technique to real-world problems). The preface quotes from An Introduction to the Bootstrap (Efron and Tibshirani, Chapman and Hall, 1993): “Our goal in this book is to arm scientists and engineers, as well as statisticians, with computational techniques that they can use to analyze and understand complicated data sets.” (p. ix). Providing these computational techniques is precisely what Zoubir and Iskander have done. Chapter 1 provides a broad-brush introduction to bootstrap techniques. Here the authors focus on differentiating bootstrap techniques from those of classical statistics, as well as differentiating bootstrap techniques from Monte Carlo ones. The main advantage of bootstrap techniques over classical statistical ones is that they can be applied to small data sets, and their main advantage over Monte Carlo techniques is that they do not assume a priori a model of system behavior or even a population distribution. Next, the chapter provides a brief description of applications in a wide variety of fields where bootstrap techniques are used. Surprisingly, applications in astrophysics (where some observed phenomena have short durations, and repeating these phenomena is difficult if not impossible) are not mentioned. The chapter ends by providing an outline of each remaining chapter. Chapter 2 starts by introducing the concept of resampling from the original dataset. This principle is then used to estimate the mean, confidence interval of the mean, probability density function, and variance of a population from a small sample. The first twenty pages of this chapter explain and, through examples, illustrate the fundamentals of non-parametric bootstrap techniques. Parametric bootstrap technique is discussed next, followed by resampling of dependent data. After that, principles of pivoting and variance stabilization are examined followed by a discussion on the limitations of bootstrap. The chapter ends by listing

1074 0090-6964/06/0600-1074/0


C 2006

Biomedical Engineering Society

Book Review

ful when working with time sensitive data, such as signal processing (as the authors illustrate in their examples), as well as econometrics and other applications that make use of time based patterns (such as trend analysis). Chapter 5 discusses five real-world applications where the authors used bootstrap analysis to draw inferences. This chapter not only brings together and reinforces the concepts discussed in earlier chapters but it also displays situations where bootstrap techniques are best suited in a variety of applications. The examples in this chapter along with the applications listed in chapter 1 highlight areas where bootstrap techniques are most entrenched today. Bootstrap techniques are also making inroads in fields as diverse as archeology, econometrics, mining/drilling, and behavioral studies. Bootstrap Techniques for Signal Processing’s real strength lies in introducing bootstrap techniques from the practitioners’ point of view. The text is written in a style that is easy to read. The authors’ liberal use of examples

1075

serves to reinforce application of the concepts presented. Procedures for using bootstrap techniques are delineated step by step in tables, thus separating them from the main body of the text and making them easy to find and reference. The text is abundantly cross-referenced making it easier for those interested in further reading to find relevant works in their areas of interest. Each chapter ends with a concise summary of the salient points discussed. This book would be an excellent text for a graduate level engineering course or a useful reference for those who wish to apply bootstrap techniques in their work. Muhammed Hassanali Morgan Electro Ceramics Bedford, Ohio 44146 Electronic-mail: [email protected]