Quantile regression for additive coefficient models in high dimensions

Zengyan Fan and Heng Lian

Journal of Multivariate Analysis, 2018, vol. 164, issue C, 54-64

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.

Keywords: Additive coefficient models; B-splines; High-dimensional model; Quantile regression; SCAD; Variable selection (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.jmva.2017.11.001

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