Permutation Methods: A Distance Function Approach (Springer Series in Statistics) - Hardcover

Mielke, Paul W. Jr.; Berry, Kenneth J.

Hardcover

ISBN 10: 0387988823 ISBN 13: 9780387988825

Publisher: Springer, 2001

Synopsis

The book will provide a comprehensive treatment of statistical inference using permutation techniques. Its purpose is to make available to practitioners a variety of useful and powerful data analytic tools that rely on very few distributional assumptions. Although many of these procedures have appeared in journal articles, they are not readily available to practitioners.

About this title

From the Back Cover

Most commonly-used parametric and permutation statistical tests, such as the matched-pairs t test and analysis of variance, are based on non-metric squared distance functions that have very poor robustness characteristics. This second edition places increased emphasis on the use of alternative permutation statistical tests based on metric Euclidean distance functions that have excellent robustness characteristics. These alternative permutation techniques provide many powerful multivariate tests including multivariate multiple regression analyses. In addition to permutation techniques described in the first edition, this second edition also contains various new permutation statistical methods and studies that include resampling multiple contingency table analyses, analysis concerns involving log-linear models with small samples, an exact discrete analog of Fisher’s continuous method for combining P-values that arise from small data sets, multiple dichotomous response analyses, problems regarding Fisher’s Z transformation for correlation analyses, and multivariate similarity comparisons between corresponding multiple categories of two samples. Paul W. Mielke, Jr. is Professor of Statistics at Colorado State University, and a fellow of the American Statistical Association. Kenneth J. Berry is Professor of Sociology at Colorado State University.

Review

From the reviews:

The authors describe permutation methods associated with completely randomized and randomized block experimental designs. Applications of the distance function permutation approach include binary and rank data. Type I error controlled regression analyses, including both prediction and linear models, are delineated. Because the regression analyses are based on a metric Euclidean distance function, special attention is paid to least sum of absolute deviations (LAD) regression. Recently developed goodness-of-fit tests, measures of agreement, multidimensional contingency table tests, and multisample univariate permutation methods are discussed and compared. The level of this monograph is that of upper division undergraduate and beginning graduate students.

--Mathematical Reviews

"It is only with the advent of powerful computing that permutation methods have become practical. The text by Mielke and Berry presents a good and accessible account of the subject to date with emphasis on the applications made easy with the developed software. ... The text covers a wide variety of topics and provides an important set of tools. It is recommended for use by graduate students and practitioners having a broad knowledge of the statistical literature." (Mayer Alvo, Sankhya: Indian Journal of Statistics, Vol. 64 (B Part 3), 2002)

"This is a book on non-parametric statistics, in particular about extending permutation methods to several contexts, notably multivariate analysis and randomized block experimental designs. ... The procedures favoured by the authors rely on general metric distance functions instead of the usual (non-metric) squared distance implied by the Normality assumption. ... anybody interested in permutation methods should find some useful material in it." (Mario Cortina Borja, Journal of Applied Statistics, Vol. 30 (5), 2003)

"Permutation methods such as the authors suggest, are generalizations of the Fisher-Pitman permutation test, which is nicely outlined ... . this is a well-written book with an intent to generalize this seemly limited tool to a lot applications." (Shin Ta Liu, Technometrics, Vol. 44 (3), 2002)

"This monograph discusses univariate and multivariate permutation tests based on distance measures. ... the book ... is well written and thorough. The material in the book is easily accessible to upper-division undergraduates and beginning graduates. Permutation Methods: A Distance Function Approach is a welcome addition to the literature on permutation tests, and the computer package available with it is an added attractive feature." (Sreenivasa Rao Jammalamadaka, Journal of the American Statistical Association, March, 2003)

"This monograph presents a fresh approach to statistical ideas based on permutation procedures. The focus is not on elaborating a mathematical theory in a theorem-proof framework. Rather it is the authors’ goal to give an overview how permutation methodology may be applied to quite different statistical questions. Most of the issues are illustrated by real data examples. Computer programs are available at the authors’ web site. ... The text can be understood without deep measure-theoretic background." (W. Stute, Zentralblatt MATH, Vol. 979, 2002)

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 0387988823
• ISBN 13: 9780387988825
• Binding: Hardcover
• Edition number: 1
• Number of pages: 352