Penalized Variable Selection in the Presence of Outliers

• Activity Number: 658 - Regression, Selection and Complex Data
• Type: Contributed
• Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
• Sponsor: International Indian Statistical Association
• Author(s): Abhijit Mandal* and Samiran Ghosh
• Companies: Wayne State University and Wayne State University
• Keywords: Penalized Variable Selection; Penalized LASSO; Robust Regression; Robust Information Criteria; M estimator

Abstract

We propose a robust variable selection procedure using a divergence based M-estimator. It produces robust estimates for the regression parameters and simultaneously selects the important explanatory variables. An efficient algorithm based on the quadratic approximation of the estimating equation is constructed. The asymptotic distribution and the influence function of the regression coefficients are derived. The widely used model selection procedures based on Mallows's Cp statistic and Akaike information criterion (AIC) often show very poor performance in the presence of heavy-tailed error or outliers. For this purpose, we introduce robust versions of these information criteria based on our proposed method. The simulation studies show that the robust variable selection outperforms the classical likelihood-based techniques in the presence of outliers. The performance of the proposed method is also explored through the real data analysis.