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

被引：3
|
作者：
Chen, Lei [1 ]
Chesneau, Christophe [2 ]
Kou, Junke [3 ]
Xu, Junlian [4 ]
机构：
[1] Baoji Univ Arts & Sci, Sch Phys & Optoelect Technol, Baoji, Peoples R China
[2] Univ Caen Normandie, LMNO, Campus 2,Sci 3, F-14032 Caen, France
[3] Guilin Univ Elect Technol, Sch Math & Computat Sci, Guilin, Peoples R China
[4] Baoji Univ Arts & Sci, Sch Math & Informat Sci, Baoji, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2023年 / 78卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Point-wise function estimation; wavelet estimator; multivariate probability density function; weighted distribution; data driven; holder space;
D O I：
10.1007/s00025-023-01846-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 Holder 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.
引用
收藏
页数：21
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