Comparison of Three Criteria for Discriminant Analysis Procedure

Abstract

This paper presents a fisher’s criterion, Welch’s criterion, and Bayes criterion for performing a discriminant analysis. These criteria estimates a linear discriminant analysis on two groups (or
regions) of contrived observations. The discriminant functions and classification rules for these criteria are also discussed. A linear discriminant analysis is performed in order to determine the
best criteria among Fisher’s criterion, Welch’s criterion and Bayes criterion by comparing their apparent error rate (APER). Any of these criteria with the least error rate is assumed to be the best criterion. After comparing their apparent error rate (APER), we observed that, the three criteria have the same confusion matrix and the same apparent error rate. Therefore we conclude that none of the three criteria is better than each other.

Key Words: Fisher’s criterion, Welch’s criterion, Bayes criterion and Apparent Error rate