Robust Variable Selection in Discriminant Analysis

• Activity Number: 519
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Stefan Van Aelst*+ and Gert Willems
• Companies: Ghent University and Ghent University
• Keywords: bootstrap ; linear discriminant analysis ; robustness ; variable selection

Abstract

We consider robust linear discriminant analysis methods that are obtained by replacing the empirical means and common covariance matrix in the classical discriminant rules by S or MM-estimates of the locations and common scatter. We discuss properties of the robust discriminant analysis and consider the problem of selecting the most relevant variables for separating the groups. To select the important variables, a robust likelihood ratio type test statistic is used in a stepwise selection procedure. To determine the thresholds for inclusion and exclusion of variables, either the asymptotic distribution of the test statistic can be used or the null distribution of the test statistic can be estimated by the fast and robust bootstrap method. The performance and robustness of this selection procedure is investigated through simulations and the method is illustrated on real data sets.