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Author:

Wang, Jinru (Wang, Jinru.) | Shi, Wenhui (Shi, Wenhui.) | Zeng, Xiaochen (Zeng, Xiaochen.)

Indexed by:

EI Scopus SCIE

Abstract:

The problem of estimating a function's derivative arises in many scientific settings, from medical imaging to astronomy. In this paper, we consider a hard thresholding wavelet approach to certain blind deconvolution problem based on the heteroscedastic data. Motivated by Delaigle & Meister's work, the adaptive wavelet estimators are proposed and their asymptotic properties are investigated. It is shown that the derivative estimators for the blind deconvolution model are spatially adaptive and attain the optimal rate of convergence up to a logarithmic factor over a range of Besov classes. Our theorems generalize the results of Cai and Navarro et al. in some sense.

Keyword:

convergence wavelet pointspread effect Besov space Gauss white noise

Author Community:

  • [ 1 ] [Wang, Jinru]Beijing Univ Technol, Fac Sci, Coll Math, Beijing 100124, Peoples R China
  • [ 2 ] [Shi, Wenhui]Beijing Univ Technol, Fac Sci, Coll Math, Beijing 100124, Peoples R China
  • [ 3 ] [Zeng, Xiaochen]Beijing Univ Technol, Fac Sci, Coll Math, Beijing 100124, Peoples R China

Reprint Author's Address:

  • [Zeng, Xiaochen]Beijing Univ Technol, Fac Sci, Coll Math, Beijing 100124, Peoples R China

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Source :

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

ISSN: 0361-0926

Year: 2020

Issue: 5

Volume: 51

Page: 1133-1154

0 . 8 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:46

Cited Count:

WoS CC Cited Count: 2

SCOPUS Cited Count: 2

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 7

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