## The Annals of Mathematical Statistics

### Tests for the Equality of Two Covariance Matrices in Relation to a Best Linear Discriminator Analysis

A. P. Dempster

#### Abstract

A pair of test statistics is proposed for the null hypothesis $\mathbf{\Sigma}_1 = \mathbf{\Sigma}_2$ when the data consists of a sample from each of the $p$-variate normal distributions $N(\mathbf{u}_1, \mathbf{\Sigma}_1)$ and $N(\mathbf{u}_2, \mathbf{\Sigma}_2)$. These tests are motivated in Section 1 and defined explicitly in Section 2. Section 3 proves a theorem which includes the null hypothesis distribution theory of the tests. Section 4 gives some details of the computation of the test statistics. An appendix describes the shadow property of concentration ellipsoids which facilitates the geometrical discussion earlier in the paper.

#### Article information

Source
Ann. Math. Statist., Volume 35, Number 1 (1964), 190-199.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177703741

Digital Object Identifier
doi:10.1214/aoms/1177703741

Mathematical Reviews number (MathSciNet)
MR161420

Zentralblatt MATH identifier
0124.09604

JSTOR