Discriminant Functions When Covariance Matrices are Unequal

Abstract This study compares by Monte Carlo methods the performance of three discriminant functions in classifying individuals into two multivariate normally distributed populations when covariance matrices are unequal—the quadratic, best linear and Fisher's linear discriminant function. The comparison is carried out both asymptotically and using samples. The expected value of the probabilities is used as the measure of performance. Parameters that are varied in the study include the distance between the populations, covariance matrices, number of dimensions, samples size and a priori probabilities of origin from the populations.