- Series: Probability and Mathematical Statistics
- Paperback: 521 pages
- Publisher: Academic Press; 1 edition (February 11, 1980)
- Language: English
- ISBN-10: 0124712525
- ISBN-13: 978-0124712522
- Product Dimensions: 6.1 x 1.2 x 9.2 inches
- Shipping Weight: 2 pounds (View shipping rates and policies)
- Average Customer Review: 6 customer reviews
- Amazon Best Sellers Rank: #1,080,590 in Books (See Top 100 in Books)
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Multivariate Analysis (Probability and Mathematical Statistics) 1st Edition
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From the Back Cover
Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between variables. Most available books on the subject concentrate on either the theoretical or the data analytic approach. This book not only combines theses two approaches but also emphasizes modern developments, so, although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, certain of the sections will commend themselves to research workers.
Broadly speaking the first half of the book contains direct extensions of univariate ideas and techniques, including exploratory data analysis, distribution theory and problems of inference. The remaining chapters concentrate on specifically multivariate problems which have no meaningful analogues in the univariate case. Topics covered include econometrics, principal component analysis, factor analysis, canonical correlation analysis, discriminate analysis, cluster analysis, multi-dimensional scaling and directional data.
Several new methods of presentation are used, for example, the data matrix is emphasized throughout, and density-free approach is given to normal theory, tests are constructed using the likelihood ratio principle and the union intersection principle, and graphical methods are used in explanation.
The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are, however, appendices which provide a sufficient background of matrix algebra, a summary of univariate statistics and some statistical tables.
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The reason I did not give if 5 is that it has started to show its age and insists that data is best arranged in rows. Those with a numerical background invariably use columns (unless they are doing funky stuff).
The description of Principal Component Analysis (PCA) is based on eigendecompositions rather than a singular value decomposition. Apart from being a numerical no-no, it is also a nice description of the data.
Every 10-20 years a statistician reinvents a minor variant of PCA (often without obvious knowledge of the previous ones). It would be nice if this was made more explicit. The connection with factor analysis is mentioned (and it has a good chapter of its own), but it would be nice to mention at least the Harkunen-Loeve and Hotelling-transform.