Smooth Tests of Goodness of Fit
Using R
2nd Edition
Published on 23. July 2009
304 pages
978-0-470-82443-6 (ISBN)
Description
In this fully revised and expanded edition of Smooth Tests ofGoodness of Fit, the latest powerful techniques for assessingstatistical and probabilistic models using this proven class ofprocedures are presented in a practical and easily accessiblemanner. Emphasis is placed on modern developments such asdata-driven tests, diagnostic properties, and model selectiontechniques. Applicable to most statistical distributions, themethodology described in this book is optimal for deriving tests offit for new distributions and complex probabilistic models, and isa standard against which new procedures should be compared.
New features of the second edition include:
* Expansion of the methodology to cover virtually any statisticaldistribution, 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 Rcode
Smooth Tests of Goodness of Fit is an invaluable resourcefor all methodological researchers as well as graduate studentsundertaking goodness-of-fit, statistical, and probabilistic modelassessment courses. Practitioners wishing to make an informedchoice of goodness-of-fit test will also find this book anindispensible guide.
Reviews of the first edition:
"This book gives a very readable account of the smooth testsof goodness of fit. The book can be read by scientists having onlyan introductory knowledge of statistics. It contains a fairlyextensive list of references; research will find it helpful for thefurther 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 ofgoodness of fit tests) are generally and easily applicable inassessing the validity of models involving statisticaldistributions....Highly recommended for undergraduate and graduatelibraries." --Choice
"The book can be read by scientists having only anintroductory knowledge of statistics. It contains a fairlyextensive list of references; researchers will find it helpful forthe further development of smooth tests."--MathematicalReviews
"Very rich in examples . . . Should find its way to the desksof many statisticians." --Technometrics
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Persons
John Rayner is a Professor of Statistics at theUniversity of Newcastle (Australia). He obtained his BA and MA from theUniversity of Sydney and PhD from theUniversity ofWollongong. He has held appointments at the Universities of New England, Otago, and Wollongong in addition to Newcastle. John is Associate Editor of the Journal of Applied Mathematics and Decision Sciences. He has over 100 publications in the fields of statistical model assessment and nonparametric statistics, has co-edited five books/proceedings/special journal issues and authored three research books.
Olivier Thas is an Associate Professor in biostatistics atGhentUniversity (Belgium). He joined the academic staff there in 1995 as a research assistant and was promoted to lecturer in 2001 after successful completion of his PhD in applied biological sciences. To-date Thas has ca. 50 publications in peer reviewed journals.
John Best is a Conjoint Academic at theUniversity ofNewcastle. After a number of years at the Commonwealth Bureau of Meterology (1967/70) and the Commonwealth Scientific and Industrial Research Organisation (CSIRO) (1970-2001) he accepted an honorary principal research fellowship at theUniversity ofWollongong (2001), where he also obtained his PhD in 1999. Best has over 100 scientific publications to his name.
Content
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 SimpleNull Hypothesis.
3.3 The Likelihood Ratio, Wald and Score Tests for CompositeNull 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 NullHypotheses.
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 NullHypotheses.
6.1 Neyman Smooth Tests for Uncategorized Composite NullHypotheses.
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 NullHypotheses.
7.1 Neyman Smooth Tests for Composite Multinomials.
7.2 Components of the Pearson-Fisher Statistic.
7.3 Composite Overlapping Cells and Cell Focusing X2Tests.
7.4 A Comparison between the Pearson-Fisher andRao-Robson X2 Tests.
8 Neyman Smooth Tests for Uncategorized Composite NullHypotheses: Discrete Distributions.
8.1 Neyman Smooth Tests for Discrete Uncategorized CompositeNull Hypotheses.
8.2 Smooth and EDF Tests for the Univariate PoissonDistribution.
8.3 Smooth and EDF Tests for the Binomial Distribution.
8.4 Smooth Tests for the Geometric Distribution.
9 Construction of Generalized Smooth Tests: TheoreticalContributions.
9.1 Introduction.
9.2 Smooth Test Statistics with Informative Decompositions.
9.3 Generalized Smooth Tests with InformativeDecompositions.
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 NullHypotheses.
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 ValueDistribution.
11.5 Generalized Smooth Tests for the Negative BinomialDistribution.
11.6 Generalized Smooth Tests for the Zero-Inflated PoissonDistribution.
11.7 Generalized Smooth Tests for the Generalized ParetoDistribution.
Appendix A: Orthonormal Polynomials and RecurrenceRelations.
Appendix B: Parametric Bootstrap p-Values.
Appendix C: Some Details for ParticularDistributions.
References.
Subject Index.
Author Index.
Example Index.
