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

by J. C. W. Rayner; O. Thas; D. J. Best

• ISBN13: 9780470824436
• ISBN10: 0470824433
• Format: eBook
• Copyright: 2009-07-01
• Publisher: Wiley

Summary

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 f8r 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

Table of Contents

Preface

Introduction

The Problem Defined

A Brief History of Smooth Tests

Monograph Outline

Examples

Pearson's X2 Test

Introduction

Foundations

The Pearson X2 Test - an Update

X2 Tests of Composite Hypotheses

Examples

Asymptotically Optimal Tests

Introduction

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

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

Generalized Score Tests

Neyman Smooth Tests for Simple Null Hypotheses

Neyman's 2 test

Neyman Smooth Tests for Uncategorized Simple Null Hypotheses

The Choice of Order

Examples

EDF Tests

Categorized Simple Null Hypotheses

Smooth Tests for Completely Specified Multinomials

X2 Effective Order

Components of X2P

Examples

Class Construction

A More Comprehensive Class of Tests

Overlapping Cells Tests

Neyman Smooth Tests for Uncategorized Composite Null Hypotheses

Neyman Smooth Tests for Uncategorized Composite Null Hypotheses

Smooth Tests for the Univariate Normal Distribution

Smooth Tests for the Exponential Distribution

Smooth Tests for Multivariate Normal Distribution

Smooth Tests for the Bivariate Poisson Distribution

Components of the Rao-Robson X2 Statistic

Neyman Smooth Tests for Categorized Composite Null Hypotheses

Neyman Smooth Tests for Composite Multinomials

Components of the Pearson-Fisher Statistic

Composite Overlapping Cells and Cell Focusing X2 Tests

A Comparison between the Pearson-Fisher and Rao-Robson X2 Tests

Neyman Smooth Tests for Uncategorized Composite Null Hypotheses: Discrete Distributions

Neyman Smooth Tests for Discrete Uncategorized Composite Null Hypotheses

Smooth and EDF Tests for the Univariate Poisson Distribution

Smooth and EDF Tests for the Binomial Distribution

Smooth Tests for the Geometric Distribution

Construction of Generalized Smooth Tests: Theoretical Contributions

Introduction

Smooth Test Statistics with Informative Decompositions

Generalized Smooth Tests with Informative Decompositions

Efficiency

Diagnostic Component Tests

Smooth Modelling

Introduction

Model Selection through Hypothesis Testing

Model Selection Based on Loss Functions

Goodness of Fit Testing after Model Selection

Correcting the Barton Density

Generalized Smooth Tests for Uncategorized Composite Null Hypotheses

Introduction

Generalized Smooth Tests for the Logistic Distribution

Generalized Smooth Tests for the Laplace Distribution

Generalized Smooth Tests for the Extreme Value Distribution

Generalized Smooth Tests for the Negative Binomial Distribution

Generalized Smooth Tests for the Zero-Inflated Poisson Distribution

Generalized Smooth Tests for the Generalized Pareto Distribution

Orthonormal Polynomials and Recurrence Relations

Parametric Bootstrap p-Values

Some Details for Particular Distributions

References

Subject Index

Author Index

Example Index

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