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Permutation Methods

A Distance Function Approach

  • Paul W. MielkeJr.
  • Kenneth J. Berry

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 1-7
  3. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 9-65
  4. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 67-112
  5. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 113-153
  6. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 155-238
  7. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 239-255
  8. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 257-307
  9. Paul W. Mielke Jr., Kenneth J. Berry
    Pages 309-317
  10. Back Matter
    Pages 319-353

About this book

Introduction

The introduction of permutation tests by R. A. Fisher relaxed the paramet­ ric structure requirement of a test statistic. For example, the structure of the test statistic is no longer required if the assumption of normality is removed. The between-object distance function of classical test statis­ tics based on the assumption of normality is squared Euclidean distance. Because squared Euclidean distance is not a metric (i. e. , the triangle in­ equality is not satisfied), it is not at all surprising that classical tests are severely affected by an extreme measurement of a single object. A major purpose of this book is to take advantage of the relaxation of the struc­ ture of a statistic allowed by permutation tests. While a variety of distance functions are valid for permutation tests, a natural choice possessing many desirable properties is ordinary (i. e. , non-squared) Euclidean distance. Sim­ ulation studies show that permutation tests based on ordinary Euclidean distance are exceedingly robust in detecting location shifts of heavy-tailed distributions. These tests depend on a metric distance function and are reasonably powerful for a broad spectrum of univariate and multivariate distributions. Least sum of absolute deviations (LAD) regression linked with a per­ mutation test based on ordinary Euclidean distance yields a linear model analysis which controls for type I error.

Keywords

Permutation Methods permutation tests regression analysis robust statistics statistical inference statistics

Authors and affiliations

  • Paul W. MielkeJr.
    • 1
  • Kenneth J. Berry
    • 2
  1. 1.Department of StatisticsColorado State UniversityFort CollinsUSA
  2. 2.Department of SociologyColorado State UniversityFort CollinsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3449-2
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-3451-5
  • Online ISBN 978-1-4757-3449-2
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site
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