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| Preface | |
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| Introduction | |
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| Decision theory | |
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| Formulation | |
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| The risk function | |
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| Criteria for a good decision rule | |
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| Randomised decision rules | |
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| Finite decision problems | |
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| Finding minimax rules in general | |
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| Admissibility of Bayes rules | |
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| Problems | |
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| Bayesian methods | |
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| Fundamental elements | |
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| The general form of Bayes rules | |
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| Back to minimax… | |
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| Shrinkage and the James-Stein estimator | |
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| Empirical Bayes | |
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| Choice of prior distributions | |
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| Computational techniques | |
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| Hierarchical modeling | |
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| Predictive distributions | |
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| Data example: Coal-mining disasters | |
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| Data example: Gene expression data | |
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| Problems | |
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| Hypothesis testing | |
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| Formulation of the hypothesis testing problem | |
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| The Neyman-Pearson Theorem | |
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| Uniformly most powerful tests | |
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| Bayes factors | |
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| Problems | |
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| Special models | |
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| Exponential families | |
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| Transformation families | |
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| Problems | |
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| Sufficiency and completeness | |
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| Definitions and elementary properties | |
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| Completeness | |
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| The Lehmann-Scheff� Theorem | |
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| Estimation with convex loss functions | |
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| Problems | |
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| Two-sided tests and conditional inference | |
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| Two-sided hypotheses and two-sided tests | |
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| Conditional inference, ancillarity and similar tests | |
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| Confidence sets | |
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| Problems | |
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| Likelihood theory | |
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| Definitions and basic properties | |
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| The Cram�r-Rao Lower Bound | |
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| Convergence of sequences of random variables | |
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| Asymptotic properties of maximum likelihood estimators | |
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| Likelihood ratio tests and Wilks' Theorem | |
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| More on multiparameter problems | |
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| Problems | |
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| Higher-order theory | |
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| Preliminaries | |
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| Parameter orthogonality | |
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| Pseudo-likelihoods | |
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| Parametrisation invariance | |
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| Edgeworth expansion | |
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| Saddlepointexpansion | |
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| Laplace approximation of integrals | |
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| The p<sup>*</sup> formula | |
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| Conditional inference in exponential families | |
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| Bartlettcorrection | |
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| Modified profile likelihood | |
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| Bayesian asymptotics | |
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| Problems | |
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| Predictive inference | |
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| Exactmethods | |
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| Decision theory approaches | |
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| Methods based on predictive likelihood | |
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| Asymptotic methods | |
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| Bootstrap methods | |
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| Conclusions and recommendations | |
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| Problems | |
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| Bootstrap methods | |
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| An inference problem | |
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| The prepivoting perspective | |
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| Data example: Bioequivalence | |
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| Further numerical illustrations | |
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| Conditional inference and the bootstrap | |
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| Problems | |
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| Bibliography | |
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| Index | |