Details

Smooth Tests of Goodness of Fit


Smooth Tests of Goodness of Fit

Using R
2. Aufl.

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

108,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 23.07.2009
ISBN/EAN: 9780470824436
Sprache: englisch
Anzahl Seiten: 320

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Beschreibungen

In this fully revised and expanded edition of <i>Smooth Tests of Goodness of Fit</i>, 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. <p>New features of the second edition include:</p> <ul type="disc"> <li>Expansion of the methodology to cover virtually any statistical distribution, including exponential families</li> <li>Discussion and application of data-driven smooth tests</li> <li>Techniques for the selection of the best model for the data, with a guide to acceptable alternatives</li> <li>Numerous new, revised, and expanded examples, generated using R code</li> </ul> <p><i>Smooth Tests of Goodness of Fit</i> 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.</p> <p><u>Reviews of the first edition:</u></p> <p>"<b>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."</b> --<i>T.K. Chandra, Zentralblatt für Mathematik und ihre Grenzgebiete, Band 73, 1/92'</i></p> <p>"<b>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</b>." --<i>Choice</i></p> <p>"<b>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</b>."--<i>Mathematical Reviews</i></p> <p>"<b>Very rich in examples . . . Should find its way to the desks of many statisticians</b>." --<i>Technometrics</i></p>
<b>Preface.</b> <p><b>1 Introduction.</b></p> <p>1.1 The Problem Defined.</p> <p>1.2 A Brief History of Smooth Tests.</p> <p>1.3 Monograph Outline.</p> <p>1.4 Examples.</p> <p><b>2 Pearson’s <i>X</i>2 Test.</b></p> <p>2.1 Introduction.</p> <p>2.2 Foundations.</p> <p>2.3 The Pearson <i>X</i>2 Test – an Update.</p> <p>2.4 <i>X</i>2 Tests of Composite Hypotheses.</p> <p>2.5 Examples.</p> <p><b>3 Asymptotically Optimal Tests.</b></p> <p>3.1 Introduction.</p> <p>3.2 The Likelihood Ratio, Wald, and Score Tests for a Simple Null Hypothesis.</p> <p>3.3 The Likelihood Ratio, Wald and Score Tests for Composite Null Hypotheses.</p> <p>3.4 Generalized Score Tests.</p> <p><b>4 Neyman Smooth Tests for Simple Null Hypotheses.</b></p> <p>4.1 Neyman’s 2 test.</p> <p>4.2 Neyman Smooth Tests for Uncategorized Simple Null Hypotheses.</p> <p>4.3 The Choice of Order.</p> <p>4.4 Examples.</p> <p>4.5 EDF Tests.</p> <p><b>5 Categorized Simple Null Hypotheses.<br /> </b></p> <p>5.1 Smooth Tests for Completely Specified Multinomials.</p> <p>5.2 <i>X</i>2 Effective Order.</p> <p>5.3 Components of <i>X</i>2<i>P.</i></p> <p>5.4 Examples.</p> <p>5.5 Class Construction.</p> <p>5.6 A More Comprehensive Class of Tests.</p> <p>5.7 Overlapping Cells Tests.</p> <p><b>6 Neyman Smooth Tests for Uncategorized Composite Null Hypotheses.</b></p> <p>6.1 Neyman Smooth Tests for Uncategorized Composite Null Hypotheses.</p> <p>6.2 Smooth Tests for the Univariate Normal Distribution.</p> <p>6.3 Smooth Tests for the Exponential Distribution.</p> <p>6.4 Smooth Tests for Multivariate Normal Distribution.</p> <p>6.5 Smooth Tests for the Bivariate Poisson Distribution.</p> <p>6.6 Components of the Rao–Robson <i>X</i>2 Statistic.</p> <p><b>7 Neyman Smooth Tests for Categorized Composite Null Hypotheses.</b></p> <p>7.1 Neyman Smooth Tests for Composite Multinomials.</p> <p>7.2 Components of the Pearson–Fisher Statistic.</p> <p>7.3 Composite Overlapping Cells and Cell Focusing <i>X</i>2 Tests.</p> <p>7.4 A Comparison between the Pearson–Fisher and Rao–Robson <i>X</i>2 Tests.</p> <p><b>8 Neyman Smooth Tests for Uncategorized Composite Null Hypotheses: Discrete Distributions.</b></p> <p>8.1 Neyman Smooth Tests for Discrete Uncategorized Composite Null Hypotheses.</p> <p>8.2 Smooth and EDF Tests for the Univariate Poisson Distribution.<br /> </p> <p>8.3 Smooth and EDF Tests for the Binomial Distribution.</p> <p>8.4 Smooth Tests for the Geometric Distribution.</p> <p><b>9 Construction of Generalized Smooth Tests: Theoretical Contributions.</b></p> <p>9.1 Introduction.</p> <p>9.2 Smooth Test Statistics with Informative Decompositions.</p> <p>9.3 Generalized Smooth Tests with Informative Decompositions.</p> <p>9.4 Efficiency.</p> <p>9.5 Diagnostic Component Tests.</p> <p><b>10 Smooth Modelling.</b></p> <p>10.1 Introduction.</p> <p>10.2 Model Selection through Hypothesis Testing.</p> <p>10.3 Model Selection Based on Loss Functions.</p> <p>10.4 Goodness of Fit Testing after Model Selection.</p> <p>10.5 Correcting the Barton Density.</p> <p><b>11 Generalized Smooth Tests for Uncategorized Composite Null Hypotheses.<br /> </b></p> <p>11.1 Introduction.</p> <p>11.2 Generalized Smooth Tests for the Logistic Distribution.</p> <p>11.3 Generalized Smooth Tests for the Laplace Distribution.</p> <p>11.4 Generalized Smooth Tests for the Extreme Value Distribution.</p> <p>11.5 Generalized Smooth Tests for the Negative Binomial Distribution.</p> <p>11.6 Generalized Smooth Tests for the Zero-Inflated Poisson Distribution.</p> <p>11.7 Generalized Smooth Tests for the Generalized Pareto Distribution.</p> <p><b>Appendix A: Orthonormal Polynomials and Recurrence Relations.</b></p> <p><b>Appendix B: Parametric Bootstrap <i>p</i>-Values.</b></p> <p><b>Appendix C: Some Details for Particular Distributions.</b></p> <p><b>References.<br /> </b></p> <p><b>Subject Index.</b></p> <p><b>Author Index.</b></p> <p><b>Example Index.</b></p>
<b>John Rayner</b> 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 <i>Journal of Applied Mathematics and Decision Sciences</i>. 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. <p><b>Olivier Thas</b> 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.</p> <p><b>John Best</b> 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.</p>
In this fully revised and expanded edition of <i>Smooth Tests of Goodness of Fit</i>, 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. <p>New features of the second edition include:</p> <ul type="disc"> <li>Expansion of the methodology to cover virtually any statistical distribution, including exponential families</li> <li>Discussion and application of data-driven smooth tests</li> <li>Techniques for the selection of the best model for the data, with a guide to acceptable alternatives</li> <li>Numerous new, revised, and expanded examples, generated using R code</li> </ul> <p><i>Smooth Tests of Goodness of Fit</i> 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.</p>

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