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An RKHS-based approach to double-penalized regression in high-dimensional partially linear models

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  • Cui, Wenquan
  • Cheng, Haoyang
  • Sun, Jiajing

Abstract

We study simultaneous variable selection and estimation in high-dimensional partially linear models under the assumption that the nonparametric component is from a reproducing kernel Hilbert space (RKHS) and that the vector of regression coefficients for the parametric component is sparse. A double penalty is used to deal with the problem. The estimate of the nonparametric component is subject to a roughness penalty based on the squared semi-norm on the RKHS, and a penalty with oracle properties is used to achieve sparsity in the parametric component. Under regularity conditions, we establish the consistency and rate of convergence of the parametric estimation together with the consistency of variable selection. The proposed estimators of the non-zero coefficients are also shown to have the asymptotic oracle property. Simulations and empirical studies illustrate the performance of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:201-210
    DOI: 10.1016/j.jmva.2018.07.013
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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. Lian, Heng & Liang, Hua, 2013. "Generalized Additive Partial Linear Models With High-Dimensional Covariates," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1136-1161, December.
    3. Ni, Xiao & Zhang, Hao Helen & Zhang, Daowen, 2009. "Automatic model selection for partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2100-2111, October.
    4. Simon N. Wood & Yannig Goude & Simon Shaw, 2015. "Generalized additive models for large data sets," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(1), pages 139-155, January.
    5. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    6. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    7. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    8. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    9. 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.
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    Cited by:

    1. 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).

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