Variable selection for nonparametric quantile regression via measurement error model

This paper proposes a variable selection procedure for the nonparametric quantile regression based on the measurement error model (MEM). The “false” Gaussian measurement error is forced into the covariates to construct a nonparametric quantile regression loss function with the MEM framework. Under this MEM framework, the variable selection procedure is completed, and the asymptotic normality of the estimates and the consistency of variable selection are verified. Some Monte Carlo simulations and a real data application are conducted to evaluate the performance of the proposed procedure.