Optimal discriminant functions for normal populations

A class of discriminant rules which includes Fisher's linear discriminant function and the likelihood ratio criterion is defined. Using asymptotic expansions of the distributions of the discriminant functions in this class, we derive a formula for cut-off points which satisfy some conditions on misclassification probabilities, and derive the optimal rules for some criteria. Some numerical experiments are carried out to examine the performance of the optimal rules for finite numbers of samples.62H30 62H20 Linear discriminant function W-rule Z-rule Asymptotic expansion