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Sparse high-dimensional semi-nonparametric quantile regression in a reproducing kernel Hilbert space

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  • Wang, Yue
  • Zhou, Yan
  • Li, Rui
  • Lian, Heng

Abstract

We consider partially linear quantile regression with a high-dimensional linear part, with the nonparametric function assumed to be in a reproducing kernel Hilbert space. We establish the overall learning rate in this setting, as well as the rate of the linear part separately. Our proof relies heavily on the empirical processes and the Rademacher complexity in the semi-nonparametric setting as analytic tools. Some simulation studies and a real data analysis are presented for illustration.

Suggested Citation

  • Wang, Yue & Zhou, Yan & Li, Rui & Lian, Heng, 2022. "Sparse high-dimensional semi-nonparametric quantile regression in a reproducing kernel Hilbert space," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:csdana:v:168:y:2022:i:c:s016794732100222x
    DOI: 10.1016/j.csda.2021.107388
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    References listed on IDEAS

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    Cited by:

    1. Bao, Yajie & Ren, Haojie, 2023. "Semi-profiled distributed estimation for high-dimensional partially linear model," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    2. Liu, Yuzi & Peng, Ling & Liu, Qing & Lian, Heng & Liu, Xiaohui, 2023. "Functional additive expectile regression in the reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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