Robust Linear Discriminant Rule using Double Trimming Location Estimator with Robust Mahalanobis Squared Distance

Abstract

The commonly employed classical linear discriminant rule, based on classical mean and covariance, are highly sensitive to outliers. Therefore, outlier influence on location and scale estimation will affect the accuracy of a discriminant rule and lead to high misclassification rates. The past studies used classical Mahalanobis Squared Distance (MSD) to alleviate the problem. However, the highly sensitive mean and covariance shortcoming can still affect the distance computation, causing masking and swamping effects. In a previous study, researchers proposed a double trimming procedure that adopted MSD-based α-trimmed mean into MSD-based α-trimmed median to construct a robust classifier. However, the proposed procedure has an overlooked flaw because the procedure employed the MSD in the computation. Thus, this study proposed to employ a robust MSD for the distance-based trimmed median procedure. The improvised trimmed median was then used to construct a robust linear discriminant rule and compared with the classical and existing robust rules using a simulation study. The results show that this study’s proposed robust linear discriminant rule has better accuracy and consistent performance than the classical linear discriminant rule and two other robust linear discriminant rules.