Annals of Statistics

The Distribution of the Characteristic Roots of $S_1S_2^{-1}$ Under Violations

K. C. S. Pillai

Abstract

The paper deals with the density of the characteristic roots of $\mathbf{S}_1\mathbf{S}_2^{-1}$ where $\mathbf{S}_1$ has a noncentral Wishart distribution, $W(p, n_1, \mathbf{\Sigma}_1, \mathbf{\Omega})$, and $\mathbf{S}_2$ has an independently distributed central Wishart distribution $W(p, n_2 \mathbf{\Sigma}_2, \mathbf{0})$, under a condition. This density is basic for an exact study of robustness of tests of at least two multivariate hypotheses.

Article information

Source
Ann. Statist., Volume 3, Number 3 (1975), 773-779.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343144

Digital Object Identifier
doi:10.1214/aos/1176343144

Mathematical Reviews number (MathSciNet)
MR370925

Zentralblatt MATH identifier
0312.62040

JSTOR
Pillai, K. C. S. The Distribution of the Characteristic Roots of $S_1S_2^{-1}$ Under Violations. Ann. Statist. 3 (1975), no. 3, 773--779. doi:10.1214/aos/1176343144. https://projecteuclid.org/euclid.aos/1176343144