Theory of point estimation
Preface to the Second Edition Preface to the First Edition List of Tables List of Figures List of Examples Table of Notation 1 Preparations 1 The Problem 2 Measure Theory and Integration 3 Probability Theory 4 Group Families 5 Exponential Families 6 Sufficient Statistics 7 Convex Loss Functions 8 Convergence in Probability and in Law 9 Problems 10 Notes 2 Unbiasedness 1 UMVU Estimators 2 Continuous One- and Two-Sample Problems 3 Discrete Distributions 4 Nonparametric Families 5 The Information Inequality 6 The Multiparameter Case and Other Extensions 7 Problems 8 Notes 3 Equivarianee 1 First Examples 2 The Principle of Equivariance 3 Location-Scale Families 4 Normal Linear Models 5 Random and Mixed Effects Models 6 Exponential Linear Models 7 Finite Population Models 8 Problems 9 Notes 4 Average Risk Optimality 1 Introduction 2 First Examples 3 Single-Prior Bayes 4 Equivariant Bayes 5 Hierarchical Bayes 6 Empirical Bayes 7 Risk Comparisons 8 Problems 9 Notes 5 Minimaxity and Admissibility 1 Minimax Estimation 2 Admissibility and Minimaxity in Exponential Families 3 Admissibility and Minimaxity in Group Families 4 Simultaneous Estimation 5 Shrinkage Estimators in the Normal Case 6 Extensions 7 Admissibility and Complete Classes 8 Problems 9 Notes 6 Asymptotic Optimality 1 Performance Evaluations in Large Samples 2 Asymptotic Efficiency 3 Efficient Likelihood Estimation 4 Likelihood Estimation: Multiple Roots 5 The Multiparameter Case 6 Applications 7 Extensions 8 Asymptotic Efficiency of Bayes Estimators 9 Problems 10 Notes References Author Index Subject Index