Lehmann E.L., Casella G. Theory of Point Estimation

2nd Edition. — Springer, 1998. — 590 p. — ISBN: 0387985026.A comprehensive account of point estimation in Euclidean sample space: Written by an acknowledged authority in the field, Theory of Point Estimation covers numerous applications to exponential and group families and offers a systematic discussion of the rich body of statistical problems relevant to these subjects.
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. Together with the author's classic volume Testing Statistical Hypotheses, Second Edition it is an outstanding text for graduate-level courses in the theory and applications of mathematical statistics.Preparations.
The Problem.
Measure Theory and Integration.
Probability Theory.
Group Families.
Exponential Families.
Sufficient Statistics.
Convex Loss Functions.
Convergence in Probability and in Law.
Unbiasedness.
UMVU Estimators.
Continuous One- and Two-Sample Problems.
Discrete Distributions.
Nonparametric Families.
The Information Inequality.
The Multiparameter Case and Other Extensions.
Equivariance.
First Examples.
The Principle of Equivariance.
Location-Scale Families.
Normal Linear Models.
Random and Mixed Effects Models.
Exponential Linear Models.
Finite Population Models.
Average Risk Optimality.First Examples.
Single-Prior Bayes.
Equivariant Bayes.
Hierarchical Bayes.
Empirical Bayes.
Risk Comparisons.
Minimaxity and Admissibility.
Minimax Estimation.
Admissibility and Minimaxity in Exponential Families.
Admissibility and Minimaxity in Group Families.
Simultaneous Estimation.
Shrinkage Estimators in the Normal Case.
Extensions.
Admissibility and Complete Classes.
Asymptotic Optimality.
Performance Evaluations in Large Samples.
Asymptotic Efficiency.
Efficient Likelihood Estimation.
Likelihood Estimation: Multiple Roots.
The Multiparameter Case.
Applications.
Extensions.
Asymptotic Efficiency of Bayes Estimators.