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Quantile regression for additive coefficient models in high dimensions

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  • Fan, Zengyan
  • Lian, Heng

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.

Suggested Citation

  • Fan, Zengyan & Lian, Heng, 2018. "Quantile regression for additive coefficient models in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 54-64.
    • Handle: RePEc:eee:jmvana:v:164:y:2018:i:c:p:54-64
    DOI: 10.1016/j.jmva.2017.11.001
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    References listed on IDEAS

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