This book is concerned with point estimation in Euclidean sample spaces.The first four chapters deal with exact (small-sample) theory, and their approach and organization parallel those of the companion volume, Testing Statistical Hypotheses (TSH). Optimal estimators are derived according to criteria such as unbiasedness, equivariance, and minimaxity, and the material is organized around these criteria. The principal applications are to exponential and group families, and the systematic discussion of the rich body of (relatively simple)statistical problems that fall under these headings constitutes a second major theme of the book.

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