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June, 1959 Applications of a Certain Representation of the Wishart Matrix
Robert A. Wijsman
Ann. Math. Statist. 30(2): 597-601 (June, 1959). DOI: 10.1214/aoms/1177706276


Apart from pre- and post-multiplication by a fixed matrix and its transpose, the Wishart matrix $\mathbf{A}$ can be written as the product of a triangular matrix and its transpose, whose elements are independent normal and chi variables. Various applications of this representation are indicated. Examples are given concerning the diagonal elements of $\mathbf{A}^{-1}$, the sample ordinary and multiple correlation coefficient, the characteristic roots of $\mathbf{A}$ and the sphericity criterion in the bivariate case.


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Robert A. Wijsman. "Applications of a Certain Representation of the Wishart Matrix." Ann. Math. Statist. 30 (2) 597 - 601, June, 1959.


Published: June, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0090.11403
MathSciNet: MR104314
Digital Object Identifier: 10.1214/aoms/1177706276

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 2 • June, 1959
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