## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Dempster, A. P. Tests for the Equality of Two Covariance Matrices in Relation to a Best Linear Discriminator Analysis. Ann. Math. Statist. 35 (1964), no. 1, 190--199. doi:10.1214/aoms/1177703741. https://projecteuclid.org/euclid.aoms/1177703741