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Author:

Wang, Zhaoliang (Wang, Zhaoliang.) | Xue, Liugen (Xue, Liugen.) (Scholars:薛留根)

Indexed by:

EI Scopus SCIE

Abstract:

This paper considers the problem of variance estimation for sparse ultra-high dimensional varying coefficient models. We first use B-spline to approximate the coefficient functions, and discuss the asymptotic behavior of a naive two-stage estimator of error variance. We also reveal that this naive estimator may significantly underestimate the error variance due to the spurious correlations, which are even higher for nonparametric models than linear models. This prompts us to propose an accurate estimator of the error variance by effectively integrating the sure independence screening and the refitted cross-validation techniques. The consistency and the asymptotic normality of the resulting estimator are established under some regularity conditions. The simulation studies are carried out to assess the finite sample performance of the proposed methods.

Keyword:

Ultra-high dimensional data Sure independence screening Variance estimation Refitted cross-validation Varying coefficient model B-spline

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 ] [Wang, Zhaoliang]Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China

Reprint Author's Address:

  • [Wang, Zhaoliang]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

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Source :

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

ISSN: 0361-0926

Year: 2019

Issue: 5

Volume: 48

Page: 1270-1283

0 . 8 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:54

Cited Count:

WoS CC Cited Count: 1

SCOPUS Cited Count: 1

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 8

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