The Annals of Mathematical Statistics

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

A. P. Dempster

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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


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