Gradient-induced Model-free Variable Selection Based on Composite Quantile Regression in Reproducing Kernel Hilbert Space

Abstract

Variable selection plays an important role to identify truly informative variables in high-dimensional data analysis. In his paper, we propose a variable selection method with composite quantile regression in reproducing kernel Hilbert space (RKHS), which has two main advantages. The first is that our method requires no special model structure assumption and no independence of error term. It is suitable for general non-parametric models and even heteroscedastic models. The second is that the calculation is simple and fast. So, it can also work in high-dimensional situations. Finally, the numerical experiments and real data analysis demonstrate its superior performance in variable selection.