In multivariate statistical analysis, elliptical distributions have
recently provided an alternative to the normal model. Most of the work,
however, is spread out in journals throughout the world and is not
easily accessible to the investigators. Fang, Kotz, and Ng presented a
systematic study of multivariate elliptical distributions, however, they
did not discuss the matrix variate case. Recently Fang and Zhang have
summarized the results of generalized multivariate analysis which
include vector as well as the matrix variate distributions. On the other
hand, Fang and Anderson collected research papers on matrix variate
elliptical distributions, many of them published for the first time in
English. They published very rich material on the topic, but the results
are given in paper form which does not provide a unified treatment of
the theory. Therefore, it seemed appropriate to collect the most
important results on the theory of matrix variate elliptically contoured
distributions available in the literature and organize them in a unified
manner that can serve as an introduction to the subject. The book will
be useful for researchers, teachers, and graduate students in statistics
and related fields whose interests involve multivariate statistical
analysis. Parts of this book were presented by Arjun K Gupta as a one
semester course at Bowling Green State University. Some new results have
also been included which generalize the results in Fang and Zhang.
Knowledge of matrix algebra and statistics at the level of Anderson is
assumed. However, Chapter 1 summarizes some results of matrix algebra.