## The Annals of Mathematical Statistics

### Discriminant Functions with Covariance

#### Abstract

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.

#### Article information

Source
Ann. Math. Statist., Volume 19, Number 2 (1948), 151-176.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177730242

Digital Object Identifier
doi:10.1214/aoms/1177730242

Mathematical Reviews number (MathSciNet)
MR25701

Zentralblatt MATH identifier
0031.37103

JSTOR