The Random-Effects Model in Discriminant Analysis

Abstract

In this article the characteristics of classical discriminant analysis under the random-effects model are investigated. Assuming that the elements within any randomly selected population are normally distributed with mean vector μ and common covariance matrix Σ , and that over different populations μ has a normal distribution with mean vector ξ and covariance matrix T , the distribution of the population-based and sample-based Mahalanobis distances between two different populations, as well as those between an observation and a randomly selected population, are derived. From these, expressions and bounds are derived for the expected probabilities of misclassification under classical discriminant analysis, applied to two- and multiple population problems respectively, when either the population-based or the sample-based linear discriminant functions are used.