點(diǎn)估計(jì)理論

前言

Since the publication in 1983 of Theory of Point Estimation, much new workhas made it desirable to bring out a second edition. The inclusion of the newmaterial has increased the length of the book from 500 to 600 pages; of theapproximately 1000 references about 25% have appeared since 1983. The greatest change has been the addition to the sparse treatment of Bayesianinference in the first edition. This includes the addition of new sections onEquivariant, Hierarchical, and Empirical Bayes, and on their comparisons. Othermajor additions deal with new developments concerning the information in-equality and simultaneous and shrinkage estimation. The Notes at the end ofeach chapter now provide not only bibliographic and historical material but alsointroductions to recent development in point estimation and other related topicswhich, for space reasons, it was not possible to include in the main text. Theproblem sections also have been greatly expanded. On the other hand, to savespace most of the discussion in the first edition on robust estimation （in particu-lar L, M, and R estimators） has been deleted. This topic is the subject of twoexcellent books by Hampel et al （1986） and Staudte and Sheather （1990）. Otherthan subject matter changes, there have been some minor modifications in thepresentation. For example, all of the references are now collected together atthe end of the text, examples are listed in a Table of Examples, and equationsare references by section and number within a chapter and by chapter, sectionand number between chapters.　The level of presentation remains the same as that of TPE. Students with athorough course in theoretical statistics （from texts such as Bickel and Doksum1977 or Casella and Berger 1990） would be well prepared. The second edition ofTPE is a companion volume to "Testing Statistical Hypotheses, Second Edition（TSH2）." Between them, they provide an account of classical statistics from aunified point of view.

內(nèi)容概要

　　Since the publication in 1983 of Theory of Point Estimation， much new workhas made it desirable to bring out a second edition. The inclusion of the newmaterial has increased the length of the book from 500 to 600 pages; of theapproximately 1000 references about 25% have appeared since 1983. The greatest change has been the addition to the sparse treatment of Bayesianinference in the first edition. This includes the addition of new sections onEquivariant， Hierarchical， and Empirical Bayes， and on their comparisons. Othermajor additions deal with new developments concerning the information in-equality and simultaneous and shrinkage estimation. The Notes at the end ofeach chapter now provide not only bibliographic and historical material but alsointroductions to recent development in point estimation and other related topicswhich， for space reasons， it was not possible to include in the main text. Theproblem sections also have been greatly expanded.

作者簡介

作者：(美國) 瓦多萊曼 (Lehmann.E.L.)

書籍目錄

Preface to the Second EditionPreface to the First EditionList of TablesList of FiguresList of ExamplesTable of Notation1 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 Notes2 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 Notes3 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 Notes4 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 Notes5 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 Notes6 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 NotesReferencesAuthor IndexSubject Index

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