A Robust Variable Selection Method for Grouped Data

• Activity Number: 377
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kristin Lilly*+ and Nedret Billor
• Companies: Auburn University and Auburn University
• Keywords: Group lasso ; robust variable selection ; multiple regression

Abstract

Group variable selection is a relatively new problem in statistics. When predictor variables can be naturally grouped in the multiple linear regression setting, the objective is to perform variable selection at the group and within-group levels. Several methods have been proposed to perform this type of variable selection, most of which are adapted from existing methods, including the group lasso. However, these methods do not perform optimally in the presence of outliers. As a result, a robust form of the group lasso is presented that is well suited to data with outliers, while still executing group variable selection. Examples with simulated data are shown to assess the performance of this newly proposed method versus existing methods when outliers are present.