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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


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.


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D. R. Jensen. "The Joint Distribution of Traces of Wishart Matrices and Some Applications." Ann. Math. Statist. 41 (1) 133 - 145, February, 1970.


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

Vol.41 • No. 1 • February, 1970
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