Preface | p. xiii |
Introduction | p. 1 |
The Problem Defined | p. 1 |
A Brief History of Smooth Tests | p. 4 |
Monograph Outline | p. 9 |
Examples | p. 10 |
Pearson's X2 Test | p. 17 |
Introduction | p. 17 |
Foundations | p. 17 |
The Pearson X2 Test - an Update | p. 19 |
Notation, Definition of the Test, and Class Construction | p. 19 |
Power Related Properties | p. 21 |
The Sample Space Partition Approach | p. 24 |
X2 Tests of Composite Hypotheses | p. 26 |
Examples | p. 27 |
Asymptotically Optimal Tests | p. 33 |
Introduction | p. 33 |
The Likelihood Ratio, Wald, and Score Tests for a Simple Null Hypothesis | p. 34 |
The Likelihood Ratio, Wald and Score Tests for Composite Null Hypotheses | p. 38 |
Generalized Score Tests | p. 47 |
Neyman Smooth Tests for Simple Null Hypotheses | p. 53 |
Neyman's ¿2 test | p. 53 |
Neyman Smooth Tests for Uncategorized Simple Null Hypotheses | p. 55 |
The Choice of Order | p. 59 |
Examples | p. 61 |
EDF Tests | p. 63 |
Categorized Simple Null Hypotheses | p. 65 |
Smooth Tests for Completely Specified Multinomials | p. 65 |
X2 Effective Order | p. 69 |
Components of X2p | p. 71 |
Construction of the Components | p. 71 |
Power Study | p. 72 |
Diagnostic Tests | p. 75 |
Cressie and Read Tests | p. 75 |
Examples | p. 76 |
Class Construction | p. 81 |
The Alternatives | p. 82 |
Results of the Simulation Study | p. 85 |
Discussion | p. 88 |
A More Comprehensive Class of Tests | p. 89 |
Overlapping Cells Tests | p. 91 |
Neyman Smooth Tests for Uncategorized Composite Null Hypotheses | p. 95 |
Neyman Smooth Tests for Uncategorized Composite Null Hypotheses | p. 95 |
Smooth Tests for the Univariate Normal Distribution | p. 102 |
The Construction of the Smooth Test | p. 102 |
Simulation Study | p. 103 |
Examples | p. 105 |
Relationship with a Test of Thomas and Pierce | p. 109 |
Smooth Tests for the Exponential Distribution | p. 109 |
Smooth Tests for Multivariate Normal Distribution | p. 122 |
Smooth Tests for the Bivariate Poisson Distribution | p. 122 |
Definitions | p. 122 |
Score Tests for the Bivariate Poisson Model | p. 123 |
A Smooth Covariance Test | p. 126 |
Variance Tests | p. 127 |
A Competitor for the Index of Dispersion Test | p. 128 |
Revised Index of Dispersion and Crockett Tests | p. 130 |
Components of the Rao-Robson X2 Statistic | p. 134 |
Neyman Smooth Tests for Categorized Composite Null Hypotheses | p. 137 |
Neyman Smooth Tests for Composite Multinomials | p. 137 |
Components of the Pearson-Fisher Statistic | p. 142 |
Composite Overlapping Cells and Cell Focusing X2 Tests | p. 144 |
A Comparison between the Pearson-Fisher and Rao-Robson X2 Tests | p. 147 |
Neyman Smooth Tests for Uncategorized Composite Null Hypotheses: Discrete Distributions | p. 151 |
Neyman Smooth Tests for Discrete Uncategorized Composite Null Hypotheses | p. 151 |
Smooth and EDF Tests for the Univariate Poisson Distribution | p. 155 |
Definitions | p. 155 |
Size and Power Study | p. 157 |
Examples | p. 160 |
Smooth and EDF Tests for the Binomial Distribution | p. 163 |
Definitions | p. 163 |
Size and Power Study | p. 165 |
Examples | p. 169 |
Smooth Tests for the Geometric Distribution | p. 170 |
Definitions | p. 170 |
Size and Power Study | p. 171 |
Examples | p. 175 |
Construction of Generalized Smooth Tests: Theoretical Contributions | p. 179 |
Introduction | p. 179 |
Smooth Test Statistics with Informative Decompositions | p. 180 |
Sufficient Condition for 'Convenient' Test Statistics | p. 180 |
Testing for an Exponential Family of Distributions | p. 181 |
Testing for Distributions not from an Exponential Family | p. 183 |
Generalized Smooth Tests with Informative Decompositions | p. 183 |
Uncategorized Distributions | p. 183 |
Categorized Distributions | p. 186 |
A Note on the Efficient Score Test | p. 187 |
Efficiency | p. 187 |
Diagnostic Component Tests | p. 189 |
Are Smooth Tests and Their Components Diagnostic? | p. 189 |
Properly Rescaled Tests | p. 190 |
Rescaling Outside Exponential Families | p. 191 |
A Simulation Study | p. 193 |
Smooth Modelling | p. 199 |
Introduction | p. 199 |
Model Selection through Hypothesis Testing | p. 201 |
Forward Selection and Backward Elimination | p. 201 |
Smooth Tests for Improved Models | p. 202 |
Examples | p. 203 |
Model Selection Based on Loss Functions | p. 206 |
Loss Functions and Expected Loss | p. 206 |
AIC and BIC | p. 208 |
Goodness of Fit Testing after Model Selection | p. 211 |
Motivation | p. 211 |
Theory | p. 212 |
Examples | p. 214 |
A Final Note | p. 218 |
Correcting the Barton Density | p. 218 |
Generalized Smooth Tests for Uncategorized Composite Null Hypotheses | p. 221 |
Introduction | p. 221 |
Generalized Smooth Tests for the Logistic Distribution | p. 224 |
Generalized Smooth Tests for the Laplace Distribution | p. 226 |
Generalized Smooth Tests for the Extreme Value Distribution | p. 229 |
Generalized Smooth Tests for the Negative Binomial Distribution | p. 232 |
Generalized Smooth Tests for the Zero-Inflated Poisson Distribution | p. 234 |
Generalized Smooth Tests for the Generalized Pareto Distribution | p. 238 |
Orthonormal Polynomials and Recurrence Relations | p. 243 |
Parametric Bootstrap p-Values | p. 247 |
Some Details for Particular Distributions | p. 249 |
The One-Parameter Logistic Distribution | p. 249 |
The Orthonormal Polynomials | p. 249 |
Estimation of the Nuisance Parameters | p. 249 |
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with ML | p. 249 |
Asymptotic Covariance Matrix of (&Vtilde;2,...,&Vtilde;4) with MOM | p. 250 |
The Two-Parameter Logistic Distribution | p. 250 |
The Orthonormal Polynomials | p. 250 |
Estimation of the Nuisance Parameters | p. 250 |
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with ML | p. 251 |
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOM | p. 251 |
The Zero-Inflated Poisson Distribution | p. 251 |
The Orthonormal Polynomials | p. 251 |
Estimation of the Nuisance Parameters | p. 252 |
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOM | p. 252 |
The Laplace Distribution | p. 253 |
The Orthonormal Polynomials | p. 253 |
Estimation of the Nuisance Parameters | p. 253 |
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with ML | p. 253 |
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOM | p. 254 |
The Extreme Value Distribution | p. 254 |
The Orthonormal Polynomials | p. 254 |
Estimation of the Nuisance Parameters | p. 254 |
Asymptotic Covariance Matrix of (&Vhat;1,...,&Vhat;4) with ML | p. 255 |
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOM | p. 255 |
The Negative Binomial Distribution | p. 255 |
The Orthonormal Polynomials | p. 255 |
Estimation of the Nuisance Parameters | p. 256 |
Asymptotic Covariance Matrix of (&Vtilde;1,...,&Vtilde;4) with ML | p. 255 |
Asymptotic Covariance Matrix of (&Vtilde;3, &Vtilde;4) with MOM | p. 255 |
The Generalized Pareto Distribution | p. 256 |
The Orthonormal Polynomials | p. 256 |
Estimation of the Nuisance Parameters | p. 257 |
Asymptotic Covariance Matrix of (&Vtilde;3,...,&Vtilde;4) with MOM | p. 257 |
References | p. 259 |
Subject Index | p. 269 |
Author Index | p. 271 |
Example Index | p. 273 |
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