The Geometry of Multivariate Statistics

by Thomas D. Wickens

A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables.

This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.

Genres: Mathematics

174 pages, Hardcover

First published December 1, 1994

Reviews

[James Carson · Rating 5 out of 5]

I can't say enough good things about this book. It admittedly doesn't cover the entire subject but fulfills its promise as a compliment to any text.
Personally, in any subject I find that study over an extended period allows perspective as I change and a variety of material offers perspective as it changes. In combination I'm left with a much broader understanding of the topic.
This text offers a quick means to achieve a fresh perspective on Multivariate Statistics. It's well worth the quick read for anyone who'd like to broaden their understanding.
Elegant, accessible, fantastic.

[William Coombs · Rating 5 out of 5]

For many years, this was my favorite nonfiction book.

[Adam · Rating 5 out of 5]

It's a very satisfying perspective on the familiar topics of intro Stats which helps them to sit well in memory and intuition; but as a lot of other people remark, its application is pretty limited and doesn't fit in the modern trends toward Bayesian and non-parametric studies, not to say anything of computer-related data analysis trends.