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9780470824429

Smooth Tests of Goodness of Fit : Using R

by ; ;
  • ISBN13:

    9780470824429

  • ISBN10:

    0470824425

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2009-06-09
  • Publisher: Wiley
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Summary

Interest in smooth tests has grown as a result of the publication of the first edition of this book and sparked interest in, for example, data-determined order of the tests, the diagnostic properties of the components of the test statistic and model selection techniques.Very practical, with numerous examples, this fully revised and updated new edition: Outlines new research, introduce new methodology and expand the contents to cover virtually any statistical distribution. Provides powerful techniques for assessment of statistical and probabilistic models, with a guide to acceptable alternatives Focuses on a class of procedures demonstrated to work well, presented in a manner that allows the development of assessment tools for new distributions and complex probabilistic models Includes online examples in RReviews 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." --TechnometricsEssential reading for Researchers and postgraduates carrying out research on goodness-of-fit, statistical and probabilistic model assessment and hypothesis testing.

Table of Contents

Prefacep. xiii
Introductionp. 1
The Problem Definedp. 1
A Brief History of Smooth Testsp. 4
Monograph Outlinep. 9
Examplesp. 10
Pearson's X2 Testp. 17
Introductionp. 17
Foundationsp. 17
The Pearson X2 Test - an Updatep. 19
Notation, Definition of the Test, and Class Constructionp. 19
Power Related Propertiesp. 21
The Sample Space Partition Approachp. 24
X2 Tests of Composite Hypothesesp. 26
Examplesp. 27
Asymptotically Optimal Testsp. 33
Introductionp. 33
The Likelihood Ratio, Wald, and Score Tests for a Simple Null Hypothesisp. 34
The Likelihood Ratio, Wald and Score Tests for Composite Null Hypothesesp. 38
Generalized Score Testsp. 47
Neyman Smooth Tests for Simple Null Hypothesesp. 53
Neyman's ¿2 testp. 53
Neyman Smooth Tests for Uncategorized Simple Null Hypothesesp. 55
The Choice of Orderp. 59
Examplesp. 61
EDF Testsp. 63
Categorized Simple Null Hypothesesp. 65
Smooth Tests for Completely Specified Multinomialsp. 65
X2 Effective Orderp. 69
Components of X2pp. 71
Construction of the Componentsp. 71
Power Studyp. 72
Diagnostic Testsp. 75
Cressie and Read Testsp. 75
Examplesp. 76
Class Constructionp. 81
The Alternativesp. 82
Results of the Simulation Studyp. 85
Discussionp. 88
A More Comprehensive Class of Testsp. 89
Overlapping Cells Testsp. 91
Neyman Smooth Tests for Uncategorized Composite Null Hypothesesp. 95
Neyman Smooth Tests for Uncategorized Composite Null Hypothesesp. 95
Smooth Tests for the Univariate Normal Distributionp. 102
The Construction of the Smooth Testp. 102
Simulation Studyp. 103
Examplesp. 105
Relationship with a Test of Thomas and Piercep. 109
Smooth Tests for the Exponential Distributionp. 109
Smooth Tests for Multivariate Normal Distributionp. 122
Smooth Tests for the Bivariate Poisson Distributionp. 122
Definitionsp. 122
Score Tests for the Bivariate Poisson Modelp. 123
A Smooth Covariance Testp. 126
Variance Testsp. 127
A Competitor for the Index of Dispersion Testp. 128
Revised Index of Dispersion and Crockett Testsp. 130
Components of the Rao-Robson X2 Statisticp. 134
Neyman Smooth Tests for Categorized Composite Null Hypothesesp. 137
Neyman Smooth Tests for Composite Multinomialsp. 137
Components of the Pearson-Fisher Statisticp. 142
Composite Overlapping Cells and Cell Focusing X2 Testsp. 144
A Comparison between the Pearson-Fisher and Rao-Robson X2 Testsp. 147
Neyman Smooth Tests for Uncategorized Composite Null Hypotheses: Discrete Distributionsp. 151
Neyman Smooth Tests for Discrete Uncategorized Composite Null Hypothesesp. 151
Smooth and EDF Tests for the Univariate Poisson Distributionp. 155
Definitionsp. 155
Size and Power Studyp. 157
Examplesp. 160
Smooth and EDF Tests for the Binomial Distributionp. 163
Definitionsp. 163
Size and Power Studyp. 165
Examplesp. 169
Smooth Tests for the Geometric Distributionp. 170
Definitionsp. 170
Size and Power Studyp. 171
Examplesp. 175
Construction of Generalized Smooth Tests: Theoretical Contributionsp. 179
Introductionp. 179
Smooth Test Statistics with Informative Decompositionsp. 180
Sufficient Condition for 'Convenient' Test Statisticsp. 180
Testing for an Exponential Family of Distributionsp. 181
Testing for Distributions not from an Exponential Familyp. 183
Generalized Smooth Tests with Informative Decompositionsp. 183
Uncategorized Distributionsp. 183
Categorized Distributionsp. 186
A Note on the Efficient Score Testp. 187
Efficiencyp. 187
Diagnostic Component Testsp. 189
Are Smooth Tests and Their Components Diagnostic?p. 189
Properly Rescaled Testsp. 190
Rescaling Outside Exponential Familiesp. 191
A Simulation Studyp. 193
Smooth Modellingp. 199
Introductionp. 199
Model Selection through Hypothesis Testingp. 201
Forward Selection and Backward Eliminationp. 201
Smooth Tests for Improved Modelsp. 202
Examplesp. 203
Model Selection Based on Loss Functionsp. 206
Loss Functions and Expected Lossp. 206
AIC and BICp. 208
Goodness of Fit Testing after Model Selectionp. 211
Motivationp. 211
Theoryp. 212
Examplesp. 214
A Final Notep. 218
Correcting the Barton Densityp. 218
Generalized Smooth Tests for Uncategorized Composite Null Hypothesesp. 221
Introductionp. 221
Generalized Smooth Tests for the Logistic Distributionp. 224
Generalized Smooth Tests for the Laplace Distributionp. 226
Generalized Smooth Tests for the Extreme Value Distributionp. 229
Generalized Smooth Tests for the Negative Binomial Distributionp. 232
Generalized Smooth Tests for the Zero-Inflated Poisson Distributionp. 234
Generalized Smooth Tests for the Generalized Pareto Distributionp. 238
Orthonormal Polynomials and Recurrence Relationsp. 243
Parametric Bootstrap p-Valuesp. 247
Some Details for Particular Distributionsp. 249
The One-Parameter Logistic Distributionp. 249
The Orthonormal Polynomialsp. 249
Estimation of the Nuisance Parametersp. 249
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with MLp. 249
Asymptotic Covariance Matrix of (&Vtilde;2,...,&Vtilde;4) with MOMp. 250
The Two-Parameter Logistic Distributionp. 250
The Orthonormal Polynomialsp. 250
Estimation of the Nuisance Parametersp. 250
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with MLp. 251
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOMp. 251
The Zero-Inflated Poisson Distributionp. 251
The Orthonormal Polynomialsp. 251
Estimation of the Nuisance Parametersp. 252
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOMp. 252
The Laplace Distributionp. 253
The Orthonormal Polynomialsp. 253
Estimation of the Nuisance Parametersp. 253
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with MLp. 253
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOMp. 254
The Extreme Value Distributionp. 254
The Orthonormal Polynomialsp. 254
Estimation of the Nuisance Parametersp. 254
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with MLp. 255
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOMp. 255
The Negative Binomial Distributionp. 255
The Orthonormal Polynomialsp. 255
Estimation of the Nuisance Parametersp. 256
Asymptotic Covariance Matrix of (&Vtilde;1,...,&Vtilde;4) with MLp. 255
Asymptotic Covariance Matrix of (&Vtilde;3, &Vtilde;4) with MOMp. 255
The Generalized Pareto Distributionp. 256
The Orthonormal Polynomialsp. 256
Estimation of the Nuisance Parametersp. 257
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOMp. 257
Referencesp. 259
Subject Indexp. 269
Author Indexp. 271
Example Indexp. 273
Table of Contents provided by Ingram. All Rights Reserved.

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