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Reviewer: Lefteris Angelis

The theory of decision making through hypotheses testing is fundamental and vital in statistical research, practice, and education. In all areas of applied science, there is an emerging demand for reducing the risk of estimations using data from experiments, measurements, and surveys. As has been recognized by decades of empirical research, real-world data rarely satisfy the usual assumptions on which traditional tests are based. Certain problems like missing and censored data, outliers, samples from mixed distributions, and complex scores defined by researchers give good reason for the development of alternative, distribution-free methods based on resampling techniques that try to reconstruct the population by drawing samples from the original sample. Permutation and bootstrap tests belong to this class of methods, which have gained much popularity in recent decades, mainly due to continuously increasing computing power, their implementation in most statistical programs, and theoretical findings that proved their efficiency. This book is the third edition of an evolving text that aims to provide a theoretical background on both parametric and resampling tests. It combines and compares these two approaches in a comprehensive manner constituting a graduate-level text, appropriate for researchers and practitioners. The content of the book is advanced and requires strong prior knowledge of probabilities and statistics. Also, knowledge of using and programming with statistical packages (for example R or Splus) is essential. The text is readable and contains a large number of examples from economics, geology, law, and clinical trials, often presented in a humorous style. Some advantages of the book are the large number of exercises in each chapter and the useful guidelines regarding which test is the most appropriate in various realistic situations. The material is organized into 14 chapters and an appendix. Chapter 1 is introductory and presents the basic statistical concepts about testing hypotheses. It starts from the fundamental notion of stochastic phenomena and proceeds with the typical notions of random variables, distribution functions, and formulation of hypotheses. The chapter closes with a brief history of the role of statistics in decision making. Chapter 2 introduces the criteria defining the optimal testing procedure and examines their interrelation. The two types of errors, the significance level, the power of a test, and the basic assumptions for testing hypotheses are discussed in detail. Elements of decision theory are provided, based on the definitions of the loss function and Bayes' risk. Chapter 3 presents a series of tests for location and scale parameters in one and two samples. Permutation, parametric, and bootstrap tests and confidence intervals are discussed thoroughly, along with their properties. Chapter 4 considers the case where the data are drawn from some common discrete and continuous probability distributions like the binomial, Poisson, exponential, uniform, and normal, and discusses the optimal tests for these data. Chapter 5 considers the problem of performing multiple tests; specifically, methods for controlling the overall error rate of multiple tests and methods for combining independent tests are reviewed. Chapters 6 and 7 are devoted to the analysis of experimental designs (like block designs and Latin squares) including multiple control variables, covariates, and restricted optimization. The analysis involves parametric analysis of variance (ANOVA) techniques and also permutation and bootstrap tests. Chapter 8 presents methods for testing hypotheses about proportions when the data are categorical, that is, the variables are either of nominal or ordinal scale. These methods are suitable for the analysis of contingency tables. In chapter 9, the analysis of multivariate data is considered. Four approaches are presented: the nonparametric combination of univariate tests, the parametric approach, permutation methods, and nonparametric runs. Also, the case of repeated measures is discussed. Chapter 10 concerns spatial-temporal data, especially the detection of clusters in time and space and the validation of some clustering models. Chapter 11 offers practical guidelines for coping with various catastrophic situations in the data, such as missing and censored data and outlying observations. Chapter 12 deals with the problem of finding optimal solutions to various test statistics for specialized situations. Permutation test statistics and bootstrap confidence intervals are discussed here. Chapter 13 provides some useful guidelines for collecting and analyzing data and for preparing reports suitable for publication. Chapter 14 discusses computational techniques appropriate for resampling methods, like Monte Carlo sampling, rapid enumeration, recursive relationships, branch and bound algorithms, Gibbs sampling, characteristic functions, Fast Fourier transforms, and asymptotic approximations. The appendix provides information on the advanced theoretical foundations of probability, measure theory, hypothesis testing, and the asymptotic behavior of resampling methods. In general, the book is recommended to researchers who use advanced statistical tests, especially those having to work with uncommon and problematic data that violate the usual assumptions. It is also a useful supplement to those using other guides or textbooks on traditional parametric and nonparametric tests. Online Computing Reviews Service