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作者:

Guo, Huijun (Guo, Huijun.) | Liu, Youming (Liu, Youming.) (学者:刘有明)

收录:

Scopus SCIE

摘要:

By developing the classical kernel method, Delaigle and Meister provide a nice estimation for a density function with some Fourier-oscillating noises over a Sobolev ball W-2(s)(L) and over L-2 risk (Delaigle and Meister in Stat. Sin. 21: 1065-1092, 2011). The current paper extends their theorem to Besov ball B-r,q(s)(L) and L-p risk with p, q, r is an element of [1,infinity] by using wavelet methods. We firstly show a linear wavelet estimation for densities in B-r,q(s)(L) over L-p risk, motivated by the work of Delaigle and Meister. Our result reduces to their theorem, when p = q = r = 2. Because the linear wavelet estimator is not adaptive, a nonlinear wavelet estimator is then provided. It turns out that the convergence rate is better than the linear one for r <= p. In addition, our conclusions contain estimations for density derivatives as well.

关键词:

Besov space density derivative density function Fourier-oscillating noises wavelet estimation

作者机构:

  • [ 1 ] [Guo, Huijun]Beijing Univ Technol, Dept Appl Math, Beijing, Peoples R China
  • [ 2 ] [Liu, Youming]Beijing Univ Technol, Dept Appl Math, Beijing, Peoples R China

通讯作者信息:

  • 刘有明

    [Liu, Youming]Beijing Univ Technol, Dept Appl Math, Pingle Yuan 100, Beijing, Peoples R China

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来源 :

JOURNAL OF INEQUALITIES AND APPLICATIONS

ISSN: 1029-242X

年份: 2014

1 . 6 0 0

JCR@2022

ESI学科: MATHEMATICS;

ESI高被引阀值:56

JCR分区:2

中科院分区:3

被引次数:

WoS核心集被引频次: 4

SCOPUS被引频次: 7

ESI高被引论文在榜: 0 展开所有

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