Quantile regression for additive coefficient models in high dimensions

Abstract

In this paper, we consider quantile regression in additive coefficient models (ACM) with high dimensionality under a sparsity assumption and approximate the additive coefficient functions by B-spline expansion. First, we consider the oracle estimator for quantile ACM when the number of additive coefficient functions is diverging. Then we adopt the SCAD penalty and investigate the non-convex penalized estimator for model estimation and variable selection. Under some regularity conditions, we prove that the oracle estimator is a local solution of the SCAD penalized quantile regression problem. Simulation studies and an application to a genome-wide association study show that the proposed method yields good numerical results.