On Median-Based Discriminant Analysis

The paper presents some useful results on the probability of misclassification when the classical linear discriminant function is replaced by a linear median discriminant function. Under a contaminated normal model, results reveal that the median-based discriminant analysis is superior to the classical linear discriminant analysis even with small amount of contamination and when the variance of the contaminating distribution is greater than or equal to 2. The small sample probability of misclassification of the classical linear discriminant analysis with unknown common variance is also derived similar to the derivation of Anderson (1978) who used the score function statistic W.

 

Keywords - median, mean, discriminant analysis, misclassification probability