On the dispersion matrix of a matrix quadratic form connected with the noncentral Wishart distribution
type: Item
instance of: scholarly article
title: On the dispersion matrix of a matrix quadratic form connected with the noncentral Wishart distribution
zbMATH Open document ID: 0611.62053
DOI: 10.1016/0024-3795(85)90057-6
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://ageconsearch.umn.edu/record/293021
review text: Recently \textit{J. R. Magnus} and the author [Ann. Stat. 7, 381-394 (1979; Zbl 0414.62040)] derived the dispersion matrix of vec X'X, when X' is a \(p\times n\) random matrix \((n>p)\) and vec X' has the distribution \({\mathcal N}_{np}(vec M',I_ n\otimes V)\). This note is concerned with the matrix quadratic form X'AX, where X' is as defined above and A is a nonrandom (not necessarily symmetric) matrix. The dispersion matrix of vec X'AX is then derived by applying results of Magnus and the author (op. cit.) and the author and \textit{T. Wansbeek} [Can. J. Stat. 11, 221- 231 (1983; Zbl 0538.15011)]. This generalizes an earlier result of \textit{M. A. Giguère} and \textit{G. P. H. Styan} [Information theory, statistical decision functions, random processes; Trans. 7th Prague Conf., Vol. B, Prague 1974, 129-139 (1978; Zbl 0406.62033)] which assumes a symmetric A.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62H99
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 3988491
zbMATH Keywords: noncentral Wishart distribution
zbMATH Keywords: Kronecker product
zbMATH Keywords: vec operator
zbMATH Keywords: matrix quadratic form
zbMATH Keywords: dispersion matrix
author: Heinz Neudecker
MaRDI profile type: Publication
OpenAlex ID: W1989779508
cites work: Q3796553
cites work: Q4192817
cites work: The commutation matrix: Some properties and applications
cites work: Some results on commutation matrices, with statistical applications
description: scientific article; zbMATH DE number 3988491