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Theory of Nonparametric Tests

  • Textbook
  • © 2018

Overview

Authors:
  1. Thorsten Dickhaus

    1. Institute for Statistics, University of Bremen, Bremen, Germany

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  • Provides a cohesive and self-contained introduction to nonparametric statistical testing
  • Includes exercises and solution tips
  • Offers a unified perspective on a variety of nonparametric test problems
  • Discusses concrete examples and computer implementations in addition to the mathematical theory

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction and Examples

    • Thorsten Dickhaus
    Pages 1-23

  3. Empirical Measures, Empirical Processes

    • Thorsten Dickhaus
    Pages 25-35

  4. Goodness-of-Fit Tests

    • Thorsten Dickhaus
    Pages 37-46

  5. Rank Tests

    • Thorsten Dickhaus
    Pages 47-69

  6. Asymptotics of Linear Resampling Statistics

    • Thorsten Dickhaus
    Pages 71-89

  7. Bootstrap Methods for Linear Models

    • Thorsten Dickhaus
    Pages 91-103

  8. Projection Tests

    • Thorsten Dickhaus
    Pages 105-118

  9. Some Extensions

    • Thorsten Dickhaus
    Pages 119-126

  10. Back Matter

    Pages 127-128
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Keywords

About this book

This textbook provides a self-contained presentation of the main concepts and methods of nonparametric statistical testing, with a particular focus on the theoretical foundations of goodness-of-fit tests, rank tests, resampling tests, and projection tests. The substitution principle is employed as a unified approach to the nonparametric test problems discussed. In addition to mathematical theory, it also includes numerous examples and computer implementations. The book is intended for advanced undergraduate, graduate, and postdoc students as well as young researchers. Readers should be familiar with the basic concepts of mathematical statistics typically covered in introductory statistics courses.

Authors and Affiliations

  • Institute for Statistics, University of Bremen, Bremen, Germany

    Thorsten Dickhaus

About the author

Thorsten Dickhaus obtained his Ph.D. in mathematics from the Heinrich Heine University, Düsseldorf, Germany in 2008. He held postdoc positions at the German Diabetes Center Düsseldorf and Berlin Institute of Technology. In 2010 he became a Junior Professor of Mathematical Statistics at the Humboldt University of Berlin, Germany. Since 2015 he has been a Full Professor of Mathematical Statistics at the University of Bremen, Germany.

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