The Matsurnoto-Yor property and the structure of the Wishart distribution

JOURNAL OF MULTIVARIATE ANALYSIS

卷:97

Article

Massam, H ; Wesolowski, J

关键词: characterization of the Wishart;    GIG distribution;    Matsumoto-Yor property;    graphical Gaussian models;   

DOI  :  10.1016/j.jmva.2004.11.008

来源: Elsevier

【 摘 要 】

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix. In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions. We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free