Theory of point estimation.

Format:

Book

Author/Creator:

Lehmann, E. L. (Erich Leo), 1917-2009.

Contributor:

Casella, George.

John G. Hartman Memorial Library Fund.

Series:

Springer texts in statistics

Language:

English

Subjects (All):

Fix-point estimation.

Genre:

Electronic books.

Physical Description:

xxvi, 589 pages : illustrations ; 24 cm.

Edition:

Second edition / E.L. Lehmann, George Casella.

Place of Publication:

New York : Springer, [1998]

Summary:

"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."--Jacket.

Contents:

1. 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. Notes

2. 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. Notes

3. Equivariance

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. Notes

4. Average Risk Optimality

1. Introduction

2. First Examples

3. Single-Prior Bayes

4. Equivariant Bayes

5. Hierarchical Bayes

6. Empirical Bayes

7. Risk Comparisons

5. 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

6. 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

10. Notes.

Notes:

Includes bibliographical references (pages 521-564) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the John G. Hartman Memorial Library Fund.

Other Format:

Printed edition

ISBN:

0387985026

9780387985022

9788181283573

8181283570

OCLC:

38833237

Publisher Number:

9780387985022

Access Restriction:

Online full text is restricted to subscribers.

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