Robustness of Variable Selection Based on Functional Response Regression Model

Function-on-scalar regression is a type of function response regression used to analyze the relationship between function response and a set of scalar predictor factors. The variable selection methods of FOSR models mostly focus on the linear effects of scalar predictor factors. Therefore, in this paper, we perform robust variable selection for nonlinear FOSR models with the presence of multiple continuous covariates to further explain the behavior of function response over time. We project functional data into a low dimensional principal component space via the principal component score of the function response, in order to use the principal component score for variable selection and regression modeling. In this paper, we develop a regularized iterative algorithm based on exponential squared loss and group smoothly clipped absolute for predicting estimates of scalar factors and function coefficients, and use tuning parameters chosen by data-driven methods to achieve robustness in variable selection. The robustness of the proposed method is verified through simulation studies and demonstrated on real datasets.