Variance components. (English) Zbl 1108.62064

Searle, Shayle R.; Casella, George; McCulloch, Charles E.

Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons (ISBN 0-470-00959-4/pbk). xxiii, 501 p. (2006).

This is the paperback-edition of the 1992 textbook by the same authors; see Zbl 0850.62007. Even the references have not been changed. In the meantime some new books on variance components and mixed linear models have appeared. We mention three of them: R. K. Burdick and F. A. Graybill, “Confidence intervals on variance components.” (1992; Zbl 0755.62055), A. I. Khuri, T. Mathew and B. K. Sinha, “Statistical tests for mixed linear models.” (1998; Zbl 0893.62009), and Poduri S. R. S. Rao, “Variance components estimation.” (1997; Zbl 0996.62501).
This books consists of 12 chapters, exercises to every chapter and a large bibliography. It starts with an introduction and historical comments. The next chapters are devoted to analysis of variance-estimation (ANOVA-estimation) in balanced and unbalanced models, including the Henderson methods. Prediction, maximum likelihood and Bayesian methods are discussed in the sequel. The last chapter on the dispersion-mean model gives a general setup for linear models. Some appendices on matrix theory and statistics are following.

Reviewer: H. Drygas (Kassel)

MSC:

62J10	Analysis of variance and covariance (ANOVA)
62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62J05	Linear regression; mixed models

Keywords:

mixed linear models; ANOVA-estimation; Henderson methods; maximum likelihood; minimum norm estimation