Some Expected Values for Probabilities of Correct Classification in Discriminant Analysis

TLDR: In this article, Monte Carlo estimates have been obtained for two quantities of interest in a discriminant analysis involving the usual linear discriminant function, the unconditional probability of correct classification and the expected value of its estimate based on the calculated Mahalanobis distance.

Abstract: Monte Carlo estimates have been obtained for two quantities of interest in a discriminant analysis involving the usual linear discriminant function. The first is the unconditional probability of correct classification; the second is the expected value of its estimate based on the calculated Mahalanobis distance. These two quantities are shown in tables and graphs versus the population Mahalanobis distance. Equal sample sizes of 25, 50, and 100 have been used in forming the discriminant functions; 2, 6, 10, 15, 20, and 30 variates have been used. A comparison is made between the Monte Carlo estimates of the unconditional probability of correct classification and an approximation suggested by Lachenbruch [41].