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Smooth Tests of Goodness of Fit: Using R, 2nd Edition

Smooth Tests of Goodness of Fit: Using R, 2nd Edition

J. C. W. Rayner, O. Thas, D. J. Best

ISBN: 978-0-470-82444-3

Jan 2010

320 pages

Select type: Online Book

Description

In this fully revised and expanded edition of Smooth Tests of Goodness of Fit, the latest powerful techniques for assessing statistical and probabilistic models using this proven class of procedures are presented in a practical and easily accessible manner. Emphasis is placed on modern developments such as data-driven tests, diagnostic properties, and model selection techniques. Applicable to most statistical distributions, the methodology described in this book is optimal for deriving tests of fit for new distributions and complex probabilistic models, and is a standard against which new procedures should be compared.

New features of the second edition include:

  • Expansion of the methodology to cover virtually any statistical distribution, including exponential families
  • Discussion and application of data-driven smooth tests
  • Techniques for the selection of the best model for the data, with a guide to acceptable alternatives
  • Numerous new, revised, and expanded examples, generated using R code

Smooth Tests of Goodness of Fit is an invaluable resource for all methodological researchers as well as graduate students undertaking goodness-of-fit, statistical, and probabilistic model assessment courses. Practitioners wishing to make an informed choice of goodness-of-fit test will also find this book an indispensible guide.

Reviews of the first edition:

"This book gives a very readable account of the smooth tests of goodness of fit. The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; research will find it helpful for the further development of smooth tests." --T.K. Chandra, Zentralblatt für Mathematik und ihre Grenzgebiete, Band 73, 1/92'

"An excellent job of showing how smooth tests (a class of goodness of fit tests) are generally and easily applicable in assessing the validity of models involving statistical distributions....Highly recommended for undergraduate and graduate libraries." --Choice

"The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; researchers will find it helpful for the further development of smooth tests."--Mathematical Reviews

"Very rich in examples . . . Should find its way to the desks of many statisticians." --Technometrics

Preface.

1 Introduction.

1.1 The Problem Defined.

1.2 A Brief History of Smooth Tests.

1.3 Monograph Outline.

1.4 Examples.

2 Pearson’s X2 Test.

2.1 Introduction.

2.2 Foundations.

2.3 The Pearson X2 Test – an Update.

2.4 X2 Tests of Composite Hypotheses.

2.5 Examples.

3 Asymptotically Optimal Tests.

3.1 Introduction.

3.2 The Likelihood Ratio, Wald, and Score Tests for a Simple Null Hypothesis.

3.3 The Likelihood Ratio, Wald and Score Tests for Composite Null Hypotheses.

3.4 Generalized Score Tests.

4 Neyman Smooth Tests for Simple Null Hypotheses.

4.1 Neyman’s 2 test.

4.2 Neyman Smooth Tests for Uncategorized Simple Null Hypotheses.

4.3 The Choice of Order.

4.4 Examples.

4.5 EDF Tests.

5 Categorized Simple Null Hypotheses.

5.1 Smooth Tests for Completely Specified Multinomials.

5.2 X2 Effective Order.

5.3 Components of X2P.

5.4 Examples.

5.5 Class Construction.

5.6 A More Comprehensive Class of Tests.

5.7 Overlapping Cells Tests.

6 Neyman Smooth Tests for Uncategorized Composite Null Hypotheses.

6.1 Neyman Smooth Tests for Uncategorized Composite Null Hypotheses.

6.2 Smooth Tests for the Univariate Normal Distribution.

6.3 Smooth Tests for the Exponential Distribution.

6.4 Smooth Tests for Multivariate Normal Distribution.

6.5 Smooth Tests for the Bivariate Poisson Distribution.

6.6 Components of the Rao–Robson X2 Statistic.

7 Neyman Smooth Tests for Categorized Composite Null Hypotheses.

7.1 Neyman Smooth Tests for Composite Multinomials.

7.2 Components of the Pearson–Fisher Statistic.

7.3 Composite Overlapping Cells and Cell Focusing X2 Tests.

7.4 A Comparison between the Pearson–Fisher and Rao–Robson X2 Tests.

8 Neyman Smooth Tests for Uncategorized Composite Null Hypotheses: Discrete Distributions.

8.1 Neyman Smooth Tests for Discrete Uncategorized Composite Null Hypotheses.

8.2 Smooth and EDF Tests for the Univariate Poisson Distribution.

8.3 Smooth and EDF Tests for the Binomial Distribution.

8.4 Smooth Tests for the Geometric Distribution.

9 Construction of Generalized Smooth Tests: Theoretical Contributions.

9.1 Introduction.

9.2 Smooth Test Statistics with Informative Decompositions.

9.3 Generalized Smooth Tests with Informative Decompositions.

9.4 Efficiency.

9.5 Diagnostic Component Tests.

10 Smooth Modelling.

10.1 Introduction.

10.2 Model Selection through Hypothesis Testing.

10.3 Model Selection Based on Loss Functions.

10.4 Goodness of Fit Testing after Model Selection.

10.5 Correcting the Barton Density.

11 Generalized Smooth Tests for Uncategorized Composite Null Hypotheses.

11.1 Introduction.

11.2 Generalized Smooth Tests for the Logistic Distribution.

11.3 Generalized Smooth Tests for the Laplace Distribution.

11.4 Generalized Smooth Tests for the Extreme Value Distribution.

11.5 Generalized Smooth Tests for the Negative Binomial Distribution.

11.6 Generalized Smooth Tests for the Zero-Inflated Poisson Distribution.

11.7 Generalized Smooth Tests for the Generalized Pareto Distribution.

Appendix A: Orthonormal Polynomials and Recurrence Relations.

Appendix B: Parametric Bootstrap p-Values.

Appendix C: Some Details for Particular Distributions.

References.

Subject Index.

Author Index.

Example Index.