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A first course in multivariate statistics. (English) Zbl 0879.62052

Springer Texts in Statistics. New York, NY: Springer. xiii, 713 p. (1997).
The book provides a unified treatment of both theoretical and practical aspects of multivariate statistics. The presentation is restricted to relatively few topics, but these are covered in detail.
The second chapter gives extensive background material on the distributions of several random variables. Then the multivariate normal distribution is dealt with in an extra chapter. This contains a short exposition of elliptical distributions also. The genuine topics of multivariate statistics which are included are discrimination and classification (lda), statistical inference for means, linear principal component analysis (pca) and normal mixtures. They are chosen because the foundation of all of them is well established and their use is unambiguous. So normal mixtures substitutes cluster analysis; factor analysis is omitted for it is believed to be of questionable value. MANOVA and logistic regression are included in one of the chapters on lda.
One of the distinguishing features is the presentation of pca through self consistency. This makes it a little bit more difficult to get into that subject. But as the author did in the whole text he derived the topic clearly and at a level that makes it accessible for students with some background in statistics. Besides the mathematically oriented aspects there are lots of explanations of applied aspects, many examples and graphical illustrations. The data analytic oriented discussions contain maximum likelihood estimation with missing data and also computer intensive methods. Each section contains exercises. Some GAUSS and MATLAB programs and all data sets are made available from a ftp site.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62H25 Factor analysis and principal components; correspondence analysis

Software:

Matlab; GAUSS; Flury
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