## The Annals of Mathematical Statistics

### The Joint Distribution of Traces of Wishart Matrices and Some Applications

D. R. Jensen

#### 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

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

#### 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

#### 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.