Multivariate permutation tests
This book provides an exposition of the use of multivariate permutation testing with particular emphasis on the use of nonparametric combination methodology. It is mostly based on the author's lecture notes for undergraduate classes in nonparametric statistics and some doctoral courses on statistics at the University of Padova. The book is divided into 12 chapters.NEWLINENEWLINENEWLINEChapter 1 contains an introduction to general aspects and principles connected with the permutation approach; among others it includes the principles of conditionality, similarity, and exchangeability. In Chapter 2, various tests are discussed for a simple example of paired data and the concept of permutation testing is intuitively explained. In Chapter 3 the theory of permutation tests for one-sample problems is formally presented. Chapter 4 contains a review of the most common multi-sample problems together with heuristic solutions. Chapter 5 provides a formal theory of permutation testing for multisample problems. This chapter includes a section on asymptotic properties of these tests. Chapter 6 concerns nonparametric combination methodology of dependent tests and provides recommendation for practical applications.NEWLINENEWLINENEWLINEChapter 7 examines several application problems solved through nonparametric combination methodology. It includes following problems: multivariate paired observations, MANOVA with continuous and/or categorical variables, goodness of fit for ordered categorical variables, and isotonic inference for categorical variables. Chapter 8 is devoted to the permutation analysis of factorial designs, while Chapter 9 concerns testing in multivariate problems. Chapter 10 discusses the multivariate Behrens-Fisher problem. Chapter 11 covers the problems of repeated measurements. Further application problems in the area of biostatistics are in in Chapter 12.NEWLINENEWLINENEWLINETypically, the structure of the chapters is the following: they start with a simple illustrative example, then a heuristic solution(s) is presented and afterwards they turn to the theoretical part. Most of the chapters are accompanied by a section with problems and excercises. The author also provides comments and remarks on related published papers and books. The reader finds also recommendations and hints concerning the computational aspects of the permutation procedures. The structure of the book allows to study it with emphasis either on the applications or/and theory. It is assumed that the reader is well acquainted with basic concepts of statistical theory, including statistical inference, nonparametric methods, concept and use of sufficiency and Monte Carlo simulation techniques.NEWLINENEWLINENEWLINERecently, the permutation approach to statistical testing problems indicates a certain comeback. This is probably happening because it appears that the permutation arguments together with proper software and fast speed computers produce quite powerful statistical procedures.NEWLINENEWLINENEWLINEThe book is well written. It can be useful (and recommended) for researchers and practitioners in a number of scientific disciplines, particularly in biostatistics, and for graduate students of both applied and theoretical statistics. It can be read with emphasis on either applications or/and theory.
scientific article; zbMATH DE number 1614565