An Introduction to Multivariate Statistical Analysis (Wiley Series in Probability and Statistics)

Rating:
Summary: Accessible. Comprehensive. Delicious.
Review: A non-esoteric introduction into the discipline of multivariate statistical theory. Accessible with undergraduate-level mathematics while retaining much of the important "guts". It's a shame that the Wiley series is often tres expensive, as opposed to budget books like Dover.

Rating:
Summary: second edition of classic multivariate text
Review: 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.

Rating:
Summary: second edition of classic multivariate text
Review: 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.