Identifying covariance differences in comparisons of linear versus quadratic classification rule

A Monte Carlo study was undertaken comparing the linear and quadratic discriminant functionin classifying individuals in two mulivariate nonmally distributed populations with unequalcovariance matrices. The conditions varied were: the covariance matrix differences, groupseparation, number of predictors, sample size, priors, and number of populations (groups). Theinternal error rate for both the linear and quadratic classification rule were compared. For allconditions, the quadratic classification rule performed better (i.e., had lower internal error rates)than the linear classification rule. The difference between the linear and quadratic classificationrules was smallest when the number of predictors was small and the variances were different.