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Numerical linear algebra for applications in statistics. (English) Zbl 0908.65015
Statistics and Computing (Cham). New York, NY: Springer. xiii, 221 p. (1998).
This book concentrates especially on the numerical aspects of linear algebra that are important to statisticians (and not only to them). Aside that the author presents some basic points from the field of computer arithmetic and some knowledge of the properties of vectors and matrices. More precisely, the first two chapters of the book are devoted to these problems. Chapters 3 and 4 cover the basic computations for the decomposition of matrices, solving linear systems and extracting eigenvalues and eigenvectors. Chapter 5 provides a brief introduction to software for computations with linear systems (IMSL libraries, Matlab, S+, etc.). Finally, in Chapter 6 a few applications in statistics are discussed.
The book is essentially self-contained, with the topics addressed constituting the essential material for a introductory course in statistical computing. The book can be also used as a supplementary reference text for a course in linear regression that emphasizes the computational aspects. Numerous exercises allow the text to be used for teaching purposes. Notice, moreover, that the prerequisites for this text are quite minimal except some background in mathematics, statistics and data analysis.
I would suggest all statisticians to read this book quite carefully. The only point that is missing is a much more detailed Chapter 6 devoted to the applications in statistics. On this place I would acknowledge to have not only 15 but at least 150 pages including detailed description of the use of all mentioned ideas in the fields of nonlinear models, robust estimation, multivariate statistics, etc.
Contents: Computer storage and manipulation of data. Basic vector/matrix computations. Solution of linear systems. Computation of eigenvectors and eigenvalues and the singular value decomposition. Software for numerical linear algebra. Applications in statistics.
Reviewer: J.Antoch (Praha)

MSC:
65Fxx Numerical linear algebra
65C99 Probabilistic methods, stochastic differential equations
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62-07 Data analysis (statistics) (MSC2010)
62J05 Linear regression; mixed models
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