Bilinear forms and zonal polynomials
This book deals with quadratic and bilinear forms in random vectors, random matrices and zonal polynomials. The contents are based on normal and elliptically contoured distributions. Many related distributions, such as matrix-variate gamma, beta distributions, Dirichlet and Wishart distributions are also dealt with. The book has five chapters: 1. Preliminaries that involve Jacobians of matrix transformations, normal, matrix-variate gamma and beta distributions; 2. Quadratic and bilinear forms in normal vectors including distributions and moments of gamma differences, bilinear forms and independence of bilinear forms; 3. Quadratic and bilinear forms in elliptically contoured distributions where results on quadratic and bilinear forms in elliptically contoured distributions are given; 4. Zonal polynomials involving zonal polynomials for quadratic and bilinear forms; 5. Generalized quadratic forms where quadratic forms are based on more general matrix distributions. The book collects most recent developments of distribution theory of matrix-variates and their quadratic and bilinear forms and is well written. There are some weaknesses. For example, there are no real applications of the theory and no material related to simulation. Although the authors collect a rich bibliography in this area, there are still missing some important references.
scientific article; zbMATH DE number 785408
scientific article