Robust Variable Selection in Functional Linear Models

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 regression and the LASSO methods have been combined (the LAD-LASSO regression method) 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 LADgroup LASSO to a functional linear regression model with a scalar response and functional predictors. We illustrate the LADgroup LASSO on both simulated and real data.