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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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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Cui, Wenquan & Cheng, Haoyang & Sun, Jiajing, 2018. "An RKHS-based approach to double-penalized regression in high-dimensional partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 201-210.
    3. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    4. Patric Müller & Sara Geer, 2015. "The Partial Linear Model in High Dimensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 580-608, June.
    5. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    8. He, Qianchuan & Kong, Linglong & Wang, Yanhua & Wang, Sijian & Chan, Timothy A. & Holland, Eric, 2016. "Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 222-239.
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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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