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Author:

Wang, Jinru (Wang, Jinru.) | Liu, Wei (Liu, Wei.)

Indexed by:

EI Scopus SCIE

Abstract:

The observed data are usually contaminated by various errors in practical applications. This paper deals with the density deconvolution problems with super smooth errors under heteroscedastic situation. We provide a new wavelet estimator and investigate its upper bound of L-p risk over Besov ball. Then the lower bound is given which shows that the defined estimator attains the optimal convergence rate. It turns out that Theorem 3.1 extends some existing theorems of Pensky and Vidakovic, Fan and Koo, as well as Li and Liu in some sense. However, since the convergence is just logarithmic rate which is not satisfactory for us. Motivated by the works of Pensky and Vidakovic, Li and Liu, we study the wavelet estimator over super smooth space to improve the convergence rate.

Keyword:

Besov space convergence rate wavelet estimator 62G07 super smooth space heteroscedastic error 62G20 42C40

Author Community:

  • [ 1 ] [Wang, Jinru]Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China
  • [ 2 ] [Liu, Wei]Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China

Reprint Author's Address:

  • [Wang, Jinru]Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China

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Source :

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

ISSN: 0361-0926

Year: 2019

Issue: 10

Volume: 48

Page: 2356-2371

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: 1

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