点推定の理論(第2版)<br>Theory of Point Estimation (Springer Texts in Statistics) (2nd ed. 1998. XXVI, 589 p. 24,5 cm)

点推定の理論(第2版)
Theory of Point Estimation (Springer Texts in Statistics) (2nd ed. 1998. XXVI, 589 p. 24,5 cm)

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  • 製本 Hardcover:ハードカバー版/ページ数 589 p.
  • 商品コード 9780387985022

Full Description


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, while 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. This is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses".

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 124 (5)
Extensions
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 322 (16)
Exponential Families
3 Admissibility and Minimaxity in Group 338 (8)
Families
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