A Data-Driven Wavelet Estimator For Deconvolution Density Estimations

This current paper provides a data-driven wavelet estimator for deconvolution density model. Moreover, we investigate the totally adaptive estimations with moderately ill-posed noises over L p risk on Besov spaces B r , q s ( R ) . Compared with the traditional adaptive wavelet estimators, the estim...

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Bibliographic Details
Published inResultate der Mathematik Vol. 78; no. 4
Main Authors Cao, Kaikai, Zeng, Xiaochen
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2023
Subjects
Mathematics
Mathematics and Statistics
Wavelets
deconvolution
62G07
data-driven
42C40
62G20
density estimation
Besov spaces
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Summary:This current paper provides a data-driven wavelet estimator for deconvolution density model. Moreover, we investigate the totally adaptive estimations with moderately ill-posed noises over L p risk on Besov spaces B r , q s ( R ) . Compared with the traditional adaptive wavelet estimators, the estimation for the case of 0 < s ≤ 1 r is considered. On the other hand, the convergence rate in the region of 1 ≤ p ≤ 2 s r + ( 2 β + 1 ) r s r + 2 β + 1 is improved than that for not necessarily compactly supported density estimations.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-023-01928-0