Bilinear forms and zonal polynomials
type: Item
instance of: scholarly article
title: Bilinear forms and zonal polynomials
zbMATH Open document ID: 0832.62044
author: Serge B. Provost
author: Takesi Hayakawa
author: Arakaparampil M. Mathai
published in: Lecture Notes in Statistics
publication date: 1995-08-15T00:00:00Z
review text: 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.
reviewed by: Kai-Tai Fang
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 785408
zbMATH Keywords: generalized quadratic forms
zbMATH Keywords: Dirichlet distributions
zbMATH Keywords: bilinear forms
zbMATH Keywords: random vectors
zbMATH Keywords: random matrices
zbMATH Keywords: zonal polynomials
zbMATH Keywords: elliptically contoured distributions
zbMATH Keywords: matrix-variate gamma
zbMATH Keywords: beta distributions
zbMATH Keywords: Wishart distributions
zbMATH Keywords: Jacobians of matrix transformations
zbMATH Keywords: quadratic forms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 785408