Effects of Sample Size Ratio on the Performance of the Quadratic Discriminant Function

Abstract

This study investigated the performance of the heteroscedastic discriminant function under the non-optimal condition of unbalanced group representation in the populations. The asymptotic performance of the classification function with respect to increased Mahalanobis’ distance (under this condition) was considered. Results obtained have shown that the misclassification of observations from the smaller group escalates when the sample size ratio 1:2 is exceeded (for small sample sizes). Results also show more sensitivity to sample size than the distance function when the data set is balanced, while the performance of the function in the classification of the underrepresented group improved by increasing the distance function. More robustness with unbalanced data was also observed with the Quadratic Function than the Linear Discriminant Function.