Wavelet Optimal Estimations for a Multivariate Probability Density Function Under Weighted Distribution

The purpose of this paper is the pointwise estimation of a multivariate probability density function with weighted distribution using wavelet methods. New theoretical contributions are provided; Point-wise convergence rates of wavelet estimators are established in the local Hölder space. First, a lo...

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Bibliographic Details
Published in:Resultate der Mathematik 2023-04, Vol.78 (2), Article 66
Main Authors: Chen, Lei, Chesneau, Christophe, Kou, Junke, Xu, Junlian
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:The purpose of this paper is the pointwise estimation of a multivariate probability density function with weighted distribution using wavelet methods. New theoretical contributions are provided; Point-wise convergence rates of wavelet estimators are established in the local Hölder space. First, a lower bound is provided for all the possible estimators. Specially, a linear wavelet estimator is defined and turned out to be the optimal one in the considered setting. Subsequently, regarding the adaptive estimation problem, a nonlinear estimator is proposed as usual and discussed. Finally, a new data driven wavelet estimator is introduced and shown to be completely adaptive and almost optimal.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-023-01846-1