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A unified penalized method for sparse additive quantile models: an RKHS approach

Author

Listed:
  • Shaogao Lv

    (Southwestern University of Finance and Economics)

  • Xin He

    (City University of Hong Kong)

  • Junhui Wang

    (City University of Hong Kong)

Abstract

This paper focuses on the high-dimensional additive quantile model, allowing for both dimension and sparsity to increase with sample size. We propose a new sparsity-smoothness penalty over a reproducing kernel Hilbert space (RKHS), which includes linear function and spline-based nonlinear function as special cases. The combination of sparsity and smoothness is crucial for the asymptotic theory as well as the computational efficiency. Oracle inequalities on excess risk of the proposed method are established under weaker conditions than most existing results. Furthermore, we develop a majorize-minimization forward splitting iterative algorithm (MMFIA) for efficient computation and investigate its numerical convergence properties. Numerical experiments are conducted on the simulated and real data examples, which support the effectiveness of the proposed method.

Suggested Citation

  • Shaogao Lv & Xin He & Junhui Wang, 2017. "A unified penalized method for sparse additive quantile models: an RKHS approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 897-923, August.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:4:d:10.1007_s10463-016-0566-9
    DOI: 10.1007/s10463-016-0566-9
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    References listed on IDEAS

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