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Author:

Cao, Kaikai (Cao, Kaikai.) | Zeng, Xiaochen (Zeng, Xiaochen.)

Indexed by:

Scopus SCIE

Abstract:

Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal Lp risk estimations over an anisotropic Nikol'skii space (Lepski, O.; Willer, T. Oracle inequalities and adaptive estimation in the convolution structure density model. Ann. Stat. 2019, 47, 233-287). Motivated by their work, we consider the same problem over Besov balls by wavelets in this paper and first provide a linear wavelet estimate. Subsequently, a non-linear wavelet estimator is introduced for adaptivity, which attains nearly-optimal convergence rates in some cases.

Keyword:

adaptive density estimation wavelet Besov space generalized deconvolution

Author Community:

  • [ 1 ] [Cao, Kaikai]Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China
  • [ 2 ] [Zeng, Xiaochen]Beijing Univ Technol, Sch Math, Fac Sci, Beijing 100124, Peoples R China

Reprint Author's Address:

  • [Cao, Kaikai]Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China

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Source :

MATHEMATICS

Year: 2020

Issue: 9

Volume: 8

2 . 4 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: 5

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