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作者:

Wang, Zhaoliang (Wang, Zhaoliang.) | Xue, Liugen (Xue, Liugen.) (学者:薛留根) | Li, Gaorong (Li, Gaorong.) (学者:李高荣) | Lu, Fei (Lu, Fei.)

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摘要:

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.

关键词:

High dimensionality Nonconvex penalty Oracle property Partially linear varying coefficient model Variable selection

作者机构:

  • [ 1 ] [Wang, Zhaoliang]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
  • [ 2 ] [Xue, Liugen]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
  • [ 3 ] [Lu, Fei]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
  • [ 4 ] [Wang, Zhaoliang]Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Peoples R China
  • [ 5 ] [Li, Gaorong]Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China

通讯作者信息:

  • [Wang, Zhaoliang]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China;;[Wang, Zhaoliang]Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Peoples R China

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来源 :

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS

ISSN: 0020-3157

年份: 2019

期: 3

卷: 71

页码: 657-677

1 . 0 0 0

JCR@2022

ESI学科: MATHEMATICS;

ESI高被引阀值:25

被引次数:

WoS核心集被引频次: 3

SCOPUS被引频次: 3

ESI高被引论文在榜: 0 展开所有

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