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

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.