The expected values of zonal polynomials of elliptically contoured distributions
type: Item
instance of: scholarly article
title: The expected values of zonal polynomials of elliptically contoured distributions
zbMATH Open document ID: 0726.60014
DOI: 10.1007/BF02006181
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1989-01-01T00:00:00Z
review text: The paper provides expressions for the expected values of zonal polynomials of matrix \(X'X\) in the case where X has a matrix elliptically contoured distribution. The work is based on results of similar nature provided by \textit{A. Constantine} [Ann. Math. Stat. 34, 1270-1285 (1963; Zbl 0123.368)], \textit{D. J. de Waal} [ibid. 43, 344-347 (1972; Zbl 0264.62017)], \textit{B. K. Shah} and \textit{C. G. Khatri} [Ann. Stat. 2, 833- 836 (1974; Zbl 0285.62026)], and \textit{R. J. Muirhead} [Aspects of multivariate statistical theory (New York, 1982)]. The examples that are provided include the multivariate t-distribution and the compound multivariate normal distribution. The fact that the expected values of the multivariate Cauchy distribution do not exist is an obvious consequence of the obtained results.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 4199142
zbMATH Keywords: Wishart distributions
zbMATH Keywords: zonal polynomials
zbMATH Keywords: matrix elliptically contoured distribution
zbMATH Keywords: multivariate t-distribution
zbMATH Keywords: multivariate Cauchy distribution
author: Jian-Lun Xu
author: Kai-Tai Fang
reviewed by: Evdokia Xekalaki
MaRDI profile type: Publication
cites work: Q3796553
cites work: Some Non-Central Distribution Problems in Multivariate Analysis
cites work: On the Expected Values of the Elementary Symmetric Functions of a Noncentral Wishart Matrix
cites work: Relationships among classes of spherical matrix distributions
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cites work: Q3219581
cites work: Proof of conjectures about the expected values of the elementary symmetric functions of a noncentral Wishart matrix
cites work: Q4723039
full work available at URL: https://doi.org/10.1007/bf02006181
OpenAlex ID: W1973270573
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description: scientific article; zbMATH DE number 4199142