Robust estimation and variable selection for function‐on‐scalar regression

Abstract

Function‐on‐scalar regression is commonly used to model the dynamic behaviour of a set of scalar predictors of interest on the functional response. In this article, we develop a robust variable selection procedure for function‐on‐scalar regression with a large number of scalar predictors based on exponential squared loss combined with the group smoothly clipped absolute deviation regularization method. The proposed procedure simultaneously selects relevant predictors and provides estimates for the functional coefficients, and achieves robustness and efficiency using tuning parameters selected by a data‐driven procedure. Under reasonable conditions, we establish the asymptotic properties of the proposed estimators, including estimation consistency and the oracle property. The finite‐sample performance of the proposed method is investigated with simulation studies. The proposed method is also demonstrated with a real diffusion tensor imaging data example.