Quantile regression for additive coefficient models in high dimensions

• Main Authors: Fan, Zengyan, Lian, Heng
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Mathematics; Additive Coefficient Models; B-splines
• Online Access: https://hdl.handle.net/10356/140938
• Institution: Nanyang Technological University

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.