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Spline estimator for ultra-high dimensional partially linear varying coefficient models

Author

Listed:
  • Zhaoliang Wang

    (Beijing University of Technology
    Henan Polytechnic University)

  • Liugen Xue

    (Beijing University of Technology)

  • Gaorong Li

    (Beijing University of Technology)

  • Fei Lu

    (Beijing University of Technology)

Abstract

In this paper, we simultaneously study variable selection and estimation problems for sparse ultra-high dimensional partially linear varying coefficient models, where the number of variables in linear part can grow much faster than the sample size while many coefficients are zeros and the dimension of nonparametric part is fixed. We apply the B-spline basis to approximate each coefficient function. First, we demonstrate the convergence rates as well as asymptotic normality of the linear coefficients for the oracle estimator when the nonzero components are known in advance. Then, we propose a nonconvex penalized estimator and derive its oracle property under mild conditions. Furthermore, we address issues of numerical implementation and of data adaptive choice of the tuning parameters. Some Monte Carlo simulations and an application to a breast cancer data set are provided to corroborate our theoretical findings in finite samples.

Suggested Citation

  • Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:3:d:10.1007_s10463-018-0654-0
    DOI: 10.1007/s10463-018-0654-0
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    References listed on IDEAS

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    1. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
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