Customer Reviews

Multivariate Analysis (Probability and Mathematical Statistics)

5 star:		(1)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

This book provides an excellent general treatment of multivariate analysis. It uses the geometric approach much more than other texts with the exception of Gnanadesikan's. It is written with elegant style. It does not describe thoroughly the multivariate normal distribution theory that one find in the classic text of Anderson. Anderson takes a much more algebraic approach and concentrates heavily on multivariate normal theory. Matrix algebra is important when studying multivaraite analysis and is particularly important if you want to read and understand Anderson. It is not as critical for this and some of the other. As with many other books on multivariate analysis, factor analysis and structural equation modelling are given little or no coverage even though they are important in applied problems. Specialized books like Harman and Bollen give a detailed treatment of factor analysis and structural equation models respectively. Also this book and many others do not cover the bootstrap methods. The bootstrap plays an important role in multivariate analysis and it is nice to see that at least Anderson gives it some coverage in the second edition of his book. This may in part be due to the fact that he is a Stanford Professor who has seen the efforts of Efron, Tibshirani and Romano on the Stanford campus.

This book gives the clearest and most elegant presentation of the theory of multivariate analysis I have seen. The reader should have a good background in linear algebra before starting this one, but with this background the authors give a very concise treatment of a large area of statistics. Many topics that are not covered in most multivariate analysis texts are covered here. The exercises are also outstanding. Many of them are very difficult and lead to more profound results. I highly recommend this text!

A very good book for someone who knows linear algebra. In fact, it is probably a good introduction to advanced statistics for someone with a numerical background.

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.