Robust Group Variable Selection Methods

• Activity Number: 240
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 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

When predictor variables possess an underlying grouping structure in multiple regression, selecting important groups of variables is an essential component of building a meaningful regression model. Some methods exist to perform group selection, but do not perform well when the data include outliers. Two methods for robust variable selection of grouped data, based on the group lasso, are presented: one which works well for data with outliers in the y-direction, and the other which works well for data with outliers in both the x- and y-directions. The effectiveness of these methods is illustrated with a simulation study and real data example. The existence of the oracle property for both methods is also investigated.