Open Access
June, 1948 Discriminant Functions with Covariance
W. G. Cochran, C. I. Bliss
Ann. Math. Statist. 19(2): 151-176 (June, 1948). DOI: 10.1214/aoms/1177730242


This paper discusses the extension of the discriminant function to the case where certain variates (called the covariance variates) are known to have the same means in all populations. Although such variates have no discriminating power by themselves, they may still be utilized in the discriminant function. The first step is to adjust the discriminators by means of their `within-sample' regressions on the covariance variates. The discriminant function is then calculated in the usual way from these adjusted variates. The standard tests of significance for the discriminant function (e.g. Hotelling's $T^2$ test) can be extended to this case without difficulty. A measure is suggested of the gain in information due to covariance and the computations are illustrated by a numerical example. The discussion is confined to the case where only a single function of the population means is being investigated.


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W. G. Cochran. C. I. Bliss. "Discriminant Functions with Covariance." Ann. Math. Statist. 19 (2) 151 - 176, June, 1948.


Published: June, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0031.37103
MathSciNet: MR25701
Digital Object Identifier: 10.1214/aoms/1177730242

Rights: Copyright © 1948 Institute of Mathematical Statistics

Vol.19 • No. 2 • June, 1948
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