The Annals of Mathematical Statistics

The Joint Distribution of Traces of Wishart Matrices and Some Applications

D. R. Jensen

Full-text: Open access

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.

Article information

Source
Ann. Math. Statist., Volume 41, Number 1 (1970), 133-145.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177697194

Digital Object Identifier
doi:10.1214/aoms/1177697194

Mathematical Reviews number (MathSciNet)
MR263201

Zentralblatt MATH identifier
0188.51703

JSTOR
links.jstor.org

Citation

Jensen, D. R. The Joint Distribution of Traces of Wishart Matrices and Some Applications. Ann. Math. Statist. 41 (1970), no. 1, 133--145. doi:10.1214/aoms/1177697194. https://projecteuclid.org/euclid.aoms/1177697194


Export citation

Corrections

  • See Correction: D. R. Jensen. Correction Note: Correction to "The Joint Distribution of Traces of Wishart Matrices and Some Applications". Ann. Math. Statist., Volume 41, Number 6 (1970), 2186--2186.