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Advanced linear models. Theory and applications. (English) Zbl 0822.62052

Statistics: Textbooks and Monographs. 141. New York, NY: Marcel Dekker, Inc. x, 560 p. (1993).
As presented in its preface, this book is intended as a textbook for a graduate course in linear models and as a reference for researchers. It covers the most up-to-date theories and methodologies, together with their applications. The book consists of ten chapters divided into three parts. All central and important topics in linear models have been discussed in detail. The titles of the three parts and 10 chapters are the following:
Part I, Preliminary results: Ch. 1, Introduction; Ch. 2, Matrix theory; Ch. 3, Multivariate normal and related distributions.
Part II, Statistical inference: Ch. 4, Introduction to linear models; Ch. 5, Parameter estimation; Ch. 6, Statistical inference.
Part III, Applications: Ch. 7, Linear regression models; Ch. 8, Analysis of variance models; Ch. 9, Analysis of covariance models; Ch. 10, Variance components models.
The book’s strength lies in matrix approach. In particular, the chapter on matrix theory (Ch. 2) covers extensive and comprehensive material. The book covers almost all recent developments in linear models, such as singular linear models, biased estimators, regression diagnostics, relative efficiency of least squares, robustness of least squares, MINQUE and so on. The authors illustrate the techniques utilizing both practical and theoretical examples.
On the whole, it is a very useful book for all persons whose are interested in linear models.
Reviewer: S.Wang (Beijing)

MSC:

62Jxx Linear inference, regression
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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