Robust Linear Discriminant Analysis with Automatic Trimmed Mean

Abstract

Linear discriminant analysis (LDA) is a multivariate statistical technique used to determine which continuous variables discriminate between two or more naturally occurring groups. This technique creates a linear discriminant function that yields optimal classification rule between two or more groups under the assumptions of normality and homoscedasticity. Nonetheless, the computation of parametric LDA which are based on the sample mean vectors and pooled sample covariance matrix are known to be sensitive to nonnormality. To overcome the sensitivity of this method towards non-normality as well as homoscedasticity, this study proposed a new robust LDA method. Through this approach, an automatic trimmed mean vector was used as a substitute for the usual mean vector in the parametric LDA. Meanwhile, for the covariance matrix, this study introduced a robust approach by multiplying the Spearman’s rho with the corresponding robust scale estimator used in the trimming process. Simulated and real financial data were used to test the performance of the proposed method in terms of misclassification rate. The results showed that the new method performed better compared to the parametric LDA and the existing robust LDA with S-estimator