Theory of Point Estimation

by ;
Edition: 2nd
Format: Hardcover
Pub. Date: 1998-08-01
Publisher(s): Springer Verlag
List Price: $149.32

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Summary

This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated. An entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. The book is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses".E.L. Lehmann is Professor Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago.George Casella is the Liberty Hyde Bailey Professor of Biological Statistics in The College of Agriculture and Life Sciences at Cornell University. Casella has served as associate editor of The American Statistician, Statistical Science and JASA. He is currently the Theory and Methods Editor of JASA. Casella has authored two other textbooks (Statistical Inference, 1990, with Roger Berger and Variance Components, 1992, with Shayle A. Searle and Charles McCulloch). He is a fellow of the IMS and ASA, and an elected fellow of the ISI.Also available:E.L. Lehmann, Testing Statistical Hypotheses Second Edition, Springer-Verlag New York, Inc., ISBN 0-387-949194.

Table of Contents

Preface to the Second Edition vii(2)
Preface to the First Edition ix(5)
List of Tables
xiv(1)
List of Figures
xv(2)
List of Examples
xvii(8)
Table of Notation
xxv
1 Preparations
1(82)
1 The Problem
1(6)
2 Measure Theory and Integration
7(6)
3 Probability Theory
13(3)
4 Group Families
16(7)
5 Exponential Families
23(9)
6 Sufficient Statistics
32(13)
7 Convex Loss Functions
45(9)
8 Convergence in Probability and in Law
54(8)
9 Problems
62(16)
10 Notes
78(5)
2 Unbiasedness
83(64)
1 UMVU Estimators
83(8)
2 Continuous One-and Two-Sample Problems
91(9)
3 Discrete Distributions
100(9)
4 Nonparametric Families
109(4)
5 The Information Inequality
113(11)
6 The Multiparameter Case and Other Extensions
124(5)
7 Problems
129(14)
8 Notes
143(4)
3 Equivariance
147(78)
1 First Examples
147(11)
2 The Principle of Equivariance
158(9)
3 Location-Scale Families
167(9)
4 Normal Linear Models
176(11)
5 Random and Mixed Effects Models
187(6)
6 Exponential Linear Models
193(5)
7 Finite Population Models
198(9)
8 Problems
207(16)
9 Notes
223(2)
4 Average Risk Optimality
225(84)
1 Introduction
225(8)
2 First Examples
233(6)
3 Single-Prior Bayes
239(6)
4 Equivariant Bayes
245(8)
5 Hierarchical Bayes
253(9)
6 Empirical Bayes
262(10)
7 Risk Comparisons
272(10)
8 Problems
282(23)
9 Notes
305(4)
5 Minimaxity and Admissibility
309(120)
1 Minimax Estimation
309(13)
2 Admissibility and Minimaxity in Exponential Families
322(16)
3 Admissibility and Minimaxity in Group Families
338(8)
4 Simultaneous Estimation
346(8)
5 Shrinkage Estimators in the Normal Case
354(12)
6 Extensions
366(10)
7 Admissibility and Complete Classes
376(13)
8 Problems
389(31)
9 Notes
420(9)
6 Asymptotic Optimality
429(92)
1 Performance Evaluations in Large Samples
429(8)
2 Asymptotic Efficiency
437(6)
3 Efficient Likelihood Estimation
443(8)
4 Likelihood Estimation: Multiple Roots
451(10)
5 The Multiparameter Case
461(7)
6 Applications
468(7)
7 Extensions
475(12)
8 Asymptotic Efficiency of Bayes Estimators
487(9)
9 Problems
496(19)
10 Notes
515(6)
References 521(44)
Author Index 565(9)
Subject Index 574

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