A One-Step Variable Selection Procedure for SCAD Penalized Quantile Regression Models

Variable selection using penalized estimation methods in quantile regression models is an important step in screening for relevant covariates. In this paper, we present a one-step estimation procedure for variable selection in sparse, linear additive quantile regression models, using the SCAD penalty. The main idea of the proposed procedure is that the usual L1-norm objective function in quantile regression estimation is replaced by a smooth parametric approximation of this function, via iterative least squares computations. We conduct a simulation study and a real data analysis to check the finite sample performance of the one-step estimator. The results reveal that the one-step quantile SCAD method identifies relevant variables efficiently even when the process under study has heavy tails or if the process is contaminated with outliers.