Variance components / Shayle R. Searle, George Casella, Charles E. McCulloch.

Format:

Book

Author/Creator:

Searle, S. R. (Shayle R.), 1928-

Contributor:

Casella, George.

McCulloch, Charles E.

Series:

Wiley series in probability and mathematical statistics. Applied probability and statistics

Language:

English

Subjects (All):

Analysis of variance.

Physical Description:

xxiii, 501 pages ; 25 cm.

Place of Publication:

New York : Wiley, [1992]

Summary:

This book presents broad coverage of variance components estimation and mixed models. Its chapters cover history (Chapter 2), analysis of variance estimation (Chapters 3, 4, and 5), maximum likelihood (ML) estimation, including restricted ML and computational methods (Chapters 6 and 8), prediction in mixed models (Chapter 7), Bayes estimation and hierarchical models (Chapter 9), categorical data (Chapter 10), covariance components and minimum norm estimation (Chapter 11), and finally, the dispersion-mean model, kurtosis and fourth moments (Chapter 12). Estimation from balanced data (having the same number of observations in the subclasses) is dealt with fully in Chapter 4, and in parts of Chapters 3 and 12; and elsewhere, estimation from unbalanced data (having unequal numbers of observations in the subclasses) is dealt with at great length with numerous details for the 1-way and 2-way classifications. This broad array of topics will appeal to research workers, to students, and to anyone interested in the use of mixed models and variance components for statistically analyzing data. The book will serve as a reference for a wide spectrum of topics for practicing statisticians. For students, it is suitable for linear models courses that include material on mixed models, variance components, and prediction. For graduate courses, there are at least four levels at which the book can be used: (I) As part of a solid linear models course use Chapters 1, 3, and 4, with 2 as supplementary reading. (II) These same chapters, presented in detail, could also be used for a 1-quarter, or slowly paced 1-semester, course on variance components. (III) An advanced course would use Chapters 1 and 2 for anintroduction, followed by an overview of Chapters 3 through 5. Then sections 8.1-8.3, Chapters 10 and 11, sections 9.1-9.4, ending with the mathematical synthesis of sections 12.1-12.5 would round out the course. (IV) Finally, the entire book would be suitable for a 2- semester or 3-quarter course. Nowhere else is there a book devoted solely to variance components with the breadth of topics found in this one.

Contents:

2. History and Comment 19

3. The 1-Way Classification 44

4. Balanced Data 112

5. Analysis of Variance Estimation for Unbalanced Data 168

6. Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) 232

7. Prediction of Random Variables 258

8. Computing ML and REML Estimates 290

9. Hierarchical Models and Bayesian Estimation 315

10. Binary and Discrete Data 367

11. Other Procedures 378

12. The Dispersion-Mean Model 405

Appendix F. Estimation Formulae for Unbalanced Data 427

Appendix M. Some Results in Matrix Algebra 442

Appendix S. Some Results in Statistics 461.

Notes:

"A Wiley-Interscience publication."

Includes bibliographical references (pages 475-489) and index.

ISBN:

0471621625 :

OCLC:

23902113