TITLE:
A One-Step Variable Selection Procedure for SCAD Penalized Quantile Regression Models
AUTHORS:
Jan G. De Gooijer
KEYWORDS:
High-Dimensional Data, Iterative Least Squares, Quantile Regression, Variable Selection
JOURNAL NAME:
Theoretical Economics Letters,
Vol.16 No.1,
January
9,
2026
ABSTRACT: 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.