
Essentials of Statistical Inference
Paperback | 29 March 2010
At a Glance
236 Pages
24.41 x 16.99 x 1.27
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Industry Reviews
'This is a solid book, ideal for advanced classes in the mathematical justification for statistical inference.' Journal of Recreational Mathematics
'I wish that I had had such a textbook during my student days ... this new book presents the core ideas of statistical inference in the unifying framework of decision theory and includes a fruitful discussion of the different foundational standpoints (Bayesian, Fisherian and frequentist) ... [it is] sufficiently precise to satisfy a mathematician and yet omitting too much technical detail that could hide the core of the ideas. Carefully selected examples from a rainbow of application areas such as baseball, coal-mining disasters or gene expression data make it even more enjoyable to read ... this book is a very nice graduate level textbook.' Journal of the Royal Statistical Society
'[This] book gives a clear and comprehensive account of the basic elements of statistical theory. It should make a good text for an advanced course on statistical inference ... Students will find it informative and challenging.' ISI Short Book Reviews
'Essentials of Statistical Inference is a book worth having.' Jane L. Harvill, Journal of the American Statistical Association
'The book is comprehensively written without dwelling in unnecessary details.' Iris Pigeot, Biometrics
'... gives a clear and comprehensive account of the basic elements of statistical theory ... a good text for an advanced course on statistical inference.' Publication of the International Statistical Institute
'The text presents the main concepts and results underlying different frameworks of inference, with particular emphasis on the contrasts among frequentist, Fisherian, and Bayesian approaches. It provides a depiction of basic material on these main approaches to inference, as well as more advanced material on recent developments in statistical theory, including higher-order likelihood inference, bootstrap methods, conditional inference, and predictive inference.' Zentralblatt MATH
| Preface | p. ix |
| Introduction | p. 1 |
| Decision theory | p. 4 |
| Formulation | p. 4 |
| The risk function | p. 5 |
| Criteria for a good decision rule | p. 7 |
| Randomised decision rules | p. 11 |
| Finite decision problems | p. 11 |
| Finding minimax rules in general | p. 18 |
| Admissibility of Bayes rules | p. 19 |
| Problems | p. 19 |
| Bayesian methods | p. 22 |
| Fundamental elements | p. 22 |
| The general form of Bayes rules | p. 28 |
| Back to minimax… | p. 32 |
| Shrinkage and the James-Stein estimator | p. 33 |
| Empirical Bayes | p. 38 |
| Choice of prior distributions | p. 39 |
| Computational techniques | p. 42 |
| Hierarchical modeling | p. 48 |
| Predictive distributions | p. 52 |
| Data example: Coal-mining disasters | p. 55 |
| Data example: Gene expression data | p. 57 |
| Problems | p. 60 |
| Hypothesis testing | p. 65 |
| Formulation of the hypothesis testing problem | p. 65 |
| The Neyman-Pearson Theorem | p. 68 |
| Uniformly most powerful tests | p. 69 |
| Bayes factors | p. 73 |
| Problems | p. 78 |
| Special models | p. 81 |
| Exponential families | p. 81 |
| Transformation families | p. 86 |
| Problems | p. 88 |
| Sufficiency and completeness | p. 90 |
| Definitions and elementary properties | p. 90 |
| Completeness | p. 94 |
| The Lehmann-Scheffé Theorem | p. 95 |
| Estimation with convex loss functions | p. 95 |
| Problems | p. 96 |
| Two-sided tests and conditional inference | p. 98 |
| Two-sided hypotheses and two-sided tests | p. 99 |
| Conditional inference, ancillarity and similar tests | p. 105 |
| Confidence sets | p. 114 |
| Problems | p. 117 |
| Likelihood theory | p. 120 |
| Definitions and basic properties | p. 120 |
| The Cramér-Rao Lower Bound | p. 125 |
| Convergence of sequences of random variables | p. 127 |
| Asymptotic properties of maximum likelihood estimators | p. 128 |
| Likelihood ratio tests and Wilks' Theorem | p. 132 |
| More on multiparameter problems | p. 134 |
| Problems | p. 137 |
| Higher-order theory | p. 140 |
| Preliminaries | p. 141 |
| Parameter orthogonality | p. 143 |
| Pseudo-likelihoods | p. 145 |
| Parametrisation invariance | p. 146 |
| Edgeworth expansion | p. 148 |
| Saddlepointexpansion | p. 149 |
| Laplace approximation of integrals | p. 152 |
| The p* formula | p. 153 |
| Conditional inference in exponential families | p. 159 |
| Bartlettcorrection | p. 160 |
| Modified profile likelihood | p. 161 |
| Bayesian asymptotics | p. 163 |
| Problems | p. 164 |
| Predictive inference | p. 169 |
| Exactmethods | p. 169 |
| Decision theory approaches | p. 172 |
| Methods based on predictive likelihood | p. 175 |
| Asymptotic methods | p. 179 |
| Bootstrap methods | p. 183 |
| Conclusions and recommendations | p. 185 |
| Problems | p. 186 |
| Bootstrap methods | p. 190 |
| An inference problem | p. 191 |
| The prepivoting perspective | p. 194 |
| Data example: Bioequivalence | p. 201 |
| Further numerical illustrations | p. 203 |
| Conditional inference and the bootstrap | p. 208 |
| Problems | p. 214 |
| Bibliography | p. 218 |
| Index | p. 223 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780521548663
ISBN-10: 0521548667
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Published: 29th March 2010
Format: Paperback
Language: English
Number of Pages: 236
Audience: General Adult
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.41 x 16.99 x 1.27
Weight (kg): 0.44
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