Variable Selection of Quantile Varying Coefficient Models Based on Kernel Smoothing

Quantile varying coefficient model is one of the robust nonparametric modeling method. When one uses varying coefficient model to analyze data, a natural question is how to simultaneously select the relevant variables and separate the nonzero constant effect variables from nonzero varying effect variables. In this paper, we address the problem of both robustness and efficiency of estimation and variable selection procedure based on quantile regression. By combining the idea of the local kernel modeling and adaptive group Lasso method, we obtain penalized estimation through imposing double penalties on the quantile check function. With appropriate selection of tuning parameters by BIC criterion, the theoretical properties of the new variable selection procedure can be established. The finite sample performance of the new method is investigated through simulation studies and the analysis of body fat data. Numerical studies show that the new method can simultaneously identify unimportant variables and separate non-varying coefficient variables among important variables without any prior information about variables and irrespective of model error distribution.