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作者:

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

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Scopus SCIE CSCD

摘要:

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).

关键词:

additive noise optimality supersmooth density wavelet estimation

作者机构:

  • [ 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

通讯作者信息:

  • 刘有明

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

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来源 :

SCIENCE CHINA-MATHEMATICS

ISSN: 1674-7283

年份: 2017

期: 10

卷: 60

页码: 1901-1922

1 . 4 0 0

JCR@2022

ESI学科: MATHEMATICS;

ESI高被引阀值:39

中科院分区:2

被引次数:

WoS核心集被引频次: 1

SCOPUS被引频次: 1

ESI高被引论文在榜: 0 展开所有

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