Robust Variable Selection for Functional Regression Models

• Activity Number: 248
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jasdeep Pannu*+ and Nedret Billor
• Companies: Auburn University and Auburn University
• Keywords: Functional Regression Model ; L1 regularization ; LAD-LASSO ; Functional variable selection ; groupLASSO ; Outliers

Abstract

We consider the problem of selecting functional variables using the L1 regularization in a functional linear regression model with a scalar response and functional predictors in the presence of outliers. Since the LASSO is a special case of the penalized least squares regression with L1-penalty function it suffers from the heavy-tailed errors and/or outliers in data. Recently the LAD-LASSO regression method is used to carry out robust parameter estimation and variable selection simultaneously for a multiple linear regression model. However variable selection of the functional predictor based on LASSO fails since multiple parameters exist for a functional predictor. Therefore group LASSO is used for selecting grouped variables rather than individual variables. In this study we extend the LAD-groupLASSO to a functional linear regression model with a scalar response and functional predictors. We illustrate the LAD-groupLASSO on both simulated and real data.