Multivariate permutation tests
type: Item
instance of: scholarly article
zbMATH Open document ID: 0972.62037
author: Fortunato Pesarin
publication date: 2001-07-05T00:00:00Z
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62-02
zbMATH DE Number: 1614565
zbMATH Keywords: Bayesian decision theory
zbMATH Keywords: subjective probability
zbMATH Keywords: foundations of statistics
MaRDI profile type: Publication
title: Multivariate permutation tests
review text: 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 illustr…
reviewed by: Marie Hušková
description: scientific article; zbMATH DE number 1614565