Robust variable selection in high-dimensional varying coefficient models based on weighted composite quantile regression

Abstract

In this paper, a new variable selection procedure based on weighted composite quantile regression is proposed for varying coefficient models with a diverging number of parameters. The proposed method is based on basis function approximation and the group SCAD penalty. The new estimation method can achieve both robustness and efficiency. Furthermore, the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation are established under some suitable assumptions. Finally, the finite sample behavior of the estimator is evaluated by simulation studies. In addition, some interesting extensions are made to separate constant coefficients from varying coefficients.