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**An Introduction to Multivariate Statistical Analysis, by T.W. Anderson**

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- Sales Rank: #7455114 in Books
- Published on: 1962
- Binding: Hardcover
- 374 pages

Most helpful customer reviews

59 of 59 people found the following review helpful.

classic text from 1958 revised

By Michael R. Chernick

The first edition of Ted Anderson’s text on multivariate analysis was published in 1959. At the time it had no rivals. This book gives a thorough mathematical treatment of classical multivariate analysis. It is extremely well organized. Development of the multivariate normal distribution and its properties are given a thorough and rigorous treatment. The Wishart distribution is derived. Properties of the multivariate normal distribution are applied to problems of classification, principal components, canonical correlation and tests of hypotheses including the use of Hotelling’s T square.

As a graduate student at Stanford, I audited Ted Anderson’s multivariate analysis course, that he taught out of the first edition of the book. It wasn’t until 1984 that he revised the text incorporating some new materials including the bootstrap method.

This is an advanced course for graduate students in statistics. It is the best source for a rigorous mathematical treatment of the important results from the theory of the multivariate normal distribution. However, it is not easy reading for someone who is interested in applications but does not have strong training in mathematics (particularly linear algebra). For applications and approaches when the normal theory doesn’t apply, the book by Gnanadesikan is very good. There are now many good theoretical and applied texts on multivariate analysis including the text by Eaton, the one by Srivastava and Khatri, one by Rencher, one by Johnson and Wichern, and the one by Mardia, Kent and Bibby. Naik and Khattree have written a very nice applied multivariate book that demonstrates the applications using SAS software every step of the way.

There are now many subspecialties including cluster analysis, principal components, correspondence analysis, factor analysis and classification that have complete texts devoted to them.

Anderson has now published a third edition to this book and it incorporates bootstrap methods

8 of 8 people found the following review helpful.

Multivariate analysis for mathematicians

By Terence Mills

I wanted to know some mathematical details from multivariate analysis. Many books on multivariate analysis are written for those who are happy to skip all these details – and often, I too am in this category. But this time I wanted proofs and mathematical explanations. I found what I wanted in Anderson’s classic text. It is a masterly work of scholarship. The author is an authority on the subject; his writing is clear – if you like reading mathematics; the proofs are there; the text contains several hundred exercises – and they are not all research level exercises; hardly any typographical errors as far as I can see. A reasonable background in linear algebra, multivariate calculus and mathematical statistics will be helpful in reading this book. I have been around long enough not to read too much into the word “introduction” used in the title. The book will not help you to learn how to use computer packages for multivariate analysis; this is a book about mathematics.

2 of 2 people found the following review helpful.

The standard in intoductory (mostly Guassian distibution) multivariate statistical analysis.

By CURE

What can U say, but Anderson is one of a couple of authors to have written seminal text on multivariate statistical analysis. One should have a background in univariate statistical analysis (e.g., Hogg, or possibly Rao). Although Anderson reviews matrix theory, at least a university level course is required. Required background also includes at least a full series of university-level calculus – multivariable and advanced – some complex variable theory would also be helpful as well as familiarity with advanced functions (e.g., Arfken). Also, it would be helpful to either read and/or have had a course in applied multivariable statistics (e.g. Johnson).

Pros:

It reviews both matrix algebra for statistics and univariate & linear models.

The text is thorough in the topics it covers.

It is terse in some of in its derivations – if that is your preference.

Anderson’s MO is an excellent balance of both mathematical rigor, but not as stifling/limited as the standard Theorem-Lemma-Corollary, etc., format.

Cons:

It is lacking on examples and applications.

This addition de-emphases some of the more modern Vec/Vech-matrix calculus that is more common in, say, modern econometrics.

Many of the derivations would be easier with a background in Fourier analysis and KL/orthogonal-function expansions.

The tables are a bit lame.

Some theorem derivations would benefit from a tensorial representation.

See all 8 customer reviews…

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