Lecture Notes in Statistics
cover

Nonparametric Monte Carlo Tests and Their Applications

Authors: Zhu, Li-Xing

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About this book

A fundamental issue in statistical analysis is testing the fit of a particular probability model to a set of observed data. Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. Nonparametric Monte Carlo Tests and Their Applications proposes a new Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. When there are no nuisance parameters to be estimated, the nonparametric Monte Carlo test can exactly maintain the significance level, and when nuisance parameters exist, this method can allow the test to asymptotically maintain the level.

The author addresses both applied and theoretical aspects of nonparametric Monte Carlo tests. The new methodology has been used for model checking in many fields of statistics, such as multivariate distribution theory, parametric and semiparametric regression models, multivariate regression models, varying-coefficient models with longitudinal data, heteroscedasticity, and homogeneity of covariance matrices. This book will be of interest to both practitioners and researchers investigating goodness-of-fit tests and resampling approximations.

Every chapter of the book includes algorithms, simulations, and theoretical deductions. The prerequisites for a full appreciation of the book are a modest knowledge of mathematical statistics and limit theorems in probability/empirical process theory. The less mathematically sophisticated reader will find Chapters 1, 2 and 6 to be a comprehensible introduction on how and where the new method can apply and the rest of the book to be a valuable reference for Monte Carlo test approximation and goodness-of-fit tests.

Lixing Zhu is Associate Professor of Statistics at the University of Hong Kong. He is a winner of the Humboldt Research Award at Alexander-von Humboldt Foundation of Germany and an elected Fellow of the Institute of Mathematical Statistics.>

Reviews

From the reviews:

"These lecture notes discuss several topics in goodness-of-fit testing, a classical area in statistical analysis. … The mathematical part contains detailed proofs of the theoretical results. Simulation studies illustrate the quality of the Monte Carlo approximation. … this book constitutes a recommendable contribution to an active area of current research." Winfried Stute for Mathematical Reviews, Issue 2006

"...Overall, this is an interesting book, which gives a nice introduction to this new and specific field of resampling methods." Dongsheng Tu for Biometrics, September 2006

"Nonparametric Monte Carlo tests (NMCT) are more and more used everywhere when standard theory fails … . The author of this concise monograph shows several fields where NMCT procedures can be effectively used … . I recommend this book not only to everybody who is deeply interested in Monte Carlo simulations but also to those interested in asymptotics and bootstrap." (Jaromir Antoch, Zentralblatt MATH, Vol. 1094 (20), 2006)


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Monte Carlo Tests

    Pages 1-9

  • Testing for Multivariate Distributions

    Pages 11-25

  • Asymptotics of Goodness-of-fit Tests for Symmetry

    Pages 27-43

  • A Test of Dimension-Reduction Type for Regressions

    Pages 45-59

  • Checking the Adequacy of a Partially Linear Model

    Pages 61-83

Buy this book

eBook 67,40 €
price for Spain (gross)
  • ISBN 978-0-387-29053-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 83,19 €
price for Spain (gross)
  • ISBN 978-0-387-25038-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Nonparametric Monte Carlo Tests and Their Applications
Authors
Series Title
Lecture Notes in Statistics
Series Volume
182
Copyright
2005
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-29053-9
DOI
10.1007/0-387-29053-2
Softcover ISBN
978-0-387-25038-0
Series ISSN
0930-0325
Edition Number
1
Number of Pages
XI, 184
Number of Illustrations
17 b/w illustrations
Topics