Title: Theory of point estimation
First published: 1983
Description: 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
Subjects: Fix-point estimation, Schätztheorie, Testtheorie, Mathematical statistics, Estimation theory, Statistics, Mathematics, Qa276.8 .l43 1983