Wishart–Laplace distributions associated with matrix quadratic forms

doi:10.1016/j.jmva.2009.12.013

Journal of Multivariate Analysis

Volume 101, Issue 5, May 2010, Pages 1168-1178

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Abstract

For a normal random matrix $Y$ with mean zero, necessary and sufficient conditions are obtained for $Y^{'} W_{k} Y$ to be Wishart–Laplace distributed and ${Y^{'} W_{k} Y}$ to be independent, where each $W_{k}$ is assumed to be symmetric rather than nonnegative definite.

AMS 2000 subject classifications

primary

62H05

secondary

62H10

Keywords

Matrix quadratic form

Laplacian distribution

Wishart distribution

Jordan algebras

Multivariate normal matrix

Cochran theorem

Cited by (0)

^☆: Research supported by NSERC Grant of Canada, PIN7914.

Journal of Multivariate Analysis

Wishart–Laplace distributions associated with matrix quadratic forms☆

Abstract

AMS 2000 subject classifications

Keywords