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Author:

Li, Rui (Li, Rui.) | Liu, YouMing (Liu, YouMing.) (Scholars:刘有明)

Indexed by:

Scopus SCIE CSCD

Abstract:

This paper studies wavelet estimations for supersmooth density functions with additive noises. We first show lower bounds of L-p risk (1 <= p < infinity) with both moderately and severely ill-posed noises. Then a Shannon wavelet estimator provides optimal or nearly-optimal estimations over L-p risks for p >= 2, and a nearly-optimal result for 1 < p < 2 under both noises. In the nearly-optimal cases, the ratios of upper and lower bounds are determined. When p = 1, we give a nearly-optimal estimation with moderately ill-posed noise by using the Meyer wavelet. Finally, the practical estimators are considered. Our results are motivated by the work of Pensky and Vidakovic (1999), Butucea and Tsybakov (2008), Comte et al. (2006), Lacour (2006) and Lounici and Nickl (2011).

Keyword:

additive noise wavelet estimation optimality supersmooth density

Author Community:

  • [ 1 ] [Li, Rui]Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China
  • [ 2 ] [Liu, YouMing]Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China
  • [ 3 ] [Li, Rui]Tianjin Univ Technol, Coll Sci, Tianjin 300384, Peoples R China

Reprint Author's Address:

  • 刘有明

    [Liu, YouMing]Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China

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Source :

SCIENCE CHINA-MATHEMATICS

ISSN: 1674-7283

Year: 2017

Issue: 10

Volume: 60

Page: 1901-1922

1 . 4 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:66

CAS Journal Grade:2

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: 10

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