[学科前沿] Theory of Point Estimation [推广有奖]

【书名】 Theory of Point Estimation
【作者】E.L. Lehmann
【出版社】Springer-Verlag
【版本】Second Edition
【出版日期】1998
【文件格式】PDF
【文件大小】2.93 MB
【页数】520 Pages
【ISBN出版号】ISBN: 978-0-387-98502-2
【资料类别】计量经济学，统计学，数学
【市面定价】65 Dollars Amazon Price
【扫描版还是影印版】影印版
【是否缺页】完整
【关键词】Point Estimation
【内容简介】

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).

【目录】

1 Preparations 1
1 The Problem 1
2 Measure Theory and Integration 7
3 Probability Theory 13
4 Group Families 16
5 Exponential Families 23
6 Sufficient Statistics 32
7 Convex Loss Functions 45
8 Convergence in Probability and in Law 54
9 Problems 62
10 Notes 78

2 Unbiasedness 83
1 UMVU Estimators 83
2 Continuous One- and Two-Sample Problems 91
3 Discrete Distributions 100
4 Nonparametric Families 109
5 The Information Inequality 113
6 The Multiparameter Case and Other Extensions 124
7 Problems 129
8 Notes 143

3 Equivariance 147
1 First Examples 147
2 The Principle of Equivariance 158
3 Location-Scale Families 167
4 Normal Linear Models 176
5 Random and Mixed Effects Models 187
6 Exponential Linear Models 193
7 Finite Population Models 198
8 Problems 207
9 Notes 223

4 Average Risk Optimality 225
1 Introduction 225
2 First Examples 233
3 Single-Prior Bayes 239
4 Equivariant Bayes 245
5 Hierarchical Bayes 253
6 Empirical Bayes 262
7 Risk Comparisons 272
8 Problems 282
9 Notes 305

5 Minimaxity and Admissibility 309
1 Minimax Estimation 309
2 Admissibility and Minimaxity in Exponential Families 322
3 Admissibility and Minimaxity in Group Families 338
4 Simultaneous Estimation 346
5 Shrinkage Estimators in the Normal Case 354
6 Extensions 366
7 Admissibility and Complete Classes 376
8 Problems 389
9 Notes 420

6 Asymptotic Optimality 429
1 Performance Evaluations in Large Samples 429
2 Asymptotic Efficiency 437
3 Efficient Likelihood Estimation 443
4 Likelihood Estimation: Multiple Roots 451
5 The Multiparameter Case 461
6 Applications 468
7 Extensions 475
8 Asymptotic Efficiency of Bayes Estimators 487
9 Problems 496
10 Notes 515
References 521
【书评】

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