Theory of Point Estimation

E.L. Lehmann, George Casella0387985026, 9780387985022

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”.

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Table of contents :
Preface to the Second Edition……Page 8
Preface to the First Edition……Page 10
Contents……Page 12
List of Tables……Page 15
List of Figures……Page 16
List of Examples……Page 18
Table of Notation……Page 26
1 The Problem……Page 28
2 Measure Theory and Integration……Page 34
3 Probability Theory……Page 40
4 Group Families……Page 43
5 Exponential Families……Page 50
6 Sufficient Statistics……Page 59
7 Convex Loss Functions……Page 72
8 Convergence in Probability and in Law……Page 81
9 Problems……Page 89
10 Notes……Page 105
1 UMVU Estimators……Page 110
2 Continuous One- and Two-Sample Problems……Page 118
3 Discrete Distributions……Page 127
4 Nonparametric Families……Page 136
5 The Information Inequality……Page 140
6 The Multiparameter Case and Other Extensions……Page 151
7 Problems……Page 156
8 Notes……Page 170
1 First Examples……Page 174
2 The Principle of Equivariance……Page 185
3 Location-Scale Families……Page 194
4 Normal Linear Models……Page 203
5 Random and Mixed Effects Models……Page 214
6 Exponential Linear Models……Page 220
7 Finite Population Models……Page 225
8 Problems……Page 234
9 Notes……Page 250
1 Introduction……Page 252
2 First Examples……Page 260
3 Single-Prior Bayes……Page 266
4 Equivariant Bayes……Page 272
5 Hierarchical Bayes……Page 280
6 Empirical Bayes……Page 289
7 Risk Comparisons……Page 299
8 Problems……Page 309
9 Notes……Page 332
1 Minimax Estimation……Page 336
2 Admissibility and Minimaxity in Exponential Families……Page 349
3 Admissibility and Minimaxity in Group Families……Page 365
4 Simultaneous Estimation……Page 373
5 Shrinkage Estimators in the Normal Case……Page 381
6 Extensions……Page 393
7 Admissibility and Complete Classes……Page 403
8 Problems……Page 416
9 Notes……Page 447
1 Performance Evaluations in Large Samples……Page 456
2 Asymptotic Efficiency……Page 464
3 Efficient Likelihood Estimation……Page 470
4 Likelihood Estimation: Multiple Roots……Page 478
5 The Multiparameter Case……Page 488
6 Applications……Page 495
7 Extensions……Page 502
8 Asymptotic Efficiency of Bayes Estimators……Page 514
9 Problems……Page 523
10 Notes……Page 542
References……Page 548
B……Page 592
D……Page 593
G……Page 594
K……Page 595
M……Page 596
P……Page 597
S……Page 598
V……Page 599
Z……Page 600
B……Page 601
C……Page 602
E……Page 604
F……Page 605
H……Page 606
J……Page 607
L……Page 608
M……Page 609
N……Page 611
P……Page 612
R……Page 613
S……Page 614
U……Page 615
W……Page 616