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Author:

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

Indexed by:

EI Scopus SCIE

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.

Keyword:

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

Author Community:

  • [ 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

Reprint Author's Address:

  • [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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Source :

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS

ISSN: 0020-3157

Year: 2019

Issue: 3

Volume: 71

Page: 657-677

1 . 0 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:54

Cited Count:

WoS CC Cited Count: 3

SCOPUS Cited Count: 3

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 6

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