Translator Disclaimer
February, 1970 The Joint Distribution of Traces of Wishart Matrices and Some Applications
D. R. Jensen
Ann. Math. Statist. 41(1): 133-145 (February, 1970). DOI: 10.1214/aoms/1177697194

Abstract

Let $\mathbf{W}_{jj}$ and $\mathbf{\Sigma}_{jj}, 1 \leqq j \leqq q$, respectively denote the diagonal blocks of a partitioned Wishart matrix $\mathbf{W}$ and its matrix $\mathbf{\Sigma}$ of parameters. A Laguerrian expansion is given for the joint distribution of $v_j = \mathrm{tr} \mathbf{W}_{jj}\mathbf{\Sigma}^{-1}_{jj}, 1 \leqq j \leqq q$, which is a generalization of known multivariate chi-square distributions. Approximations to the joint distribution function are discussed, and probability inequalities are given for this and a related multivariate $F$-distribution. Applications are made to some simultaneous multivariate test procedures.

Citation

Download Citation

D. R. Jensen. "The Joint Distribution of Traces of Wishart Matrices and Some Applications." Ann. Math. Statist. 41 (1) 133 - 145, February, 1970. https://doi.org/10.1214/aoms/1177697194

Information

Published: February, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0188.51703
MathSciNet: MR263201
Digital Object Identifier: 10.1214/aoms/1177697194

Rights: Copyright © 1970 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.41 • No. 1 • February, 1970
Back to Top