Rank Based Group Variable Selection for Functional Linear Model

Abstract

We propose a robust rank based variable selection method for a functional linear regression model with multiple explanatory functions and a scalar response. The procedure extends rank based group variable selection to functional variable selection and the proposed estimator is robust in the presence of outliers in predictor function space as well as response space. The performance of the proposed robust method is demonstrated with an extensive simulation study and real data examples. We prove the proposed method with a group-adaptive penalty achieves the oracle property.