On Robustifying the Fisher’s Discriminant Function using L – Estimators

Abstract

Multivariate data can be classified into different groups. One useful statistical tool for classification is discriminant analysis whose major objective is to classify data into different populations based on a training sample. The problem arises when the data contain outliers which greatly affect the classification performance. Some studies used robust L-estimators such as median, truncated mean, trimean, and winsorized mean, yielding a robust version of Fisher’s Discriminant Function. In this study, the total probability of misclassification is computed through a simulation experiment using MATLAB to examine the behavior of the L-estimators. Relative efficiencies are determined to compare the efficiency of the estimators. Results showed that, when using the robust L-estimators, the classification performance of the discriminant rules improved, and among the estimators, median is appropriate for classifying observations but the classification efficiency is limited. L-estimators outperformed the classical in terms of the relative efficiency. Among the L-estimators, winsorized mean is more stable in terms of classification efficiency.