The Random-Effects Model in Discriminant Analysis

Abstract

In th is thesis the characteristics o f discriminant analysis under the random effects model are investigated.Assuming tha t the elements w ithin any randomly selected population are normally distributed with mean vector y and common covariance matrix E, and th a t over d iffe re n t populations p has a normal d istrib utio n with mean vector % and covariance matrix T, the distributions o f the popula tion-based and sample-based Mahalanobis distances between two d iffe re n t populations are derived. From these, expressions and bounds are derived fo r the expeeW probabilities o f mis-and correct cla ssifica tion under classical discriminant analysis, applied to two-and k-population problems respectively, when using eithe r the population-based or sample-based lin e a r discriminant functions.