The optimal wavelet estimation for biased density

被引：0
|
作者：
Xu, Junlian [1 ]
机构：
[1] Baoji Univ Arts & Sci, Sch Math & Informat Sci, Baoji, Peoples R China
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2022年 / 51卷 / 24期
关键词：
Wavelet estimator; biased density; pointwise estimation; optimality; adaptivity; local Hö lder space;
D O I：
10.1080/03610926.2021.1905845
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, the optimal estimation at a given point is considered for biased density in theory. A lower bound is first provided for all possible estimators over the local Holder space. Using wavelet method, a linear wavelet estimator is constructed and turned out to be optimal by investigating its upper bound of pointwise convergence rate. To get the adaptivity, a nonlinear wavelet estimator is obtained and proved to be near-optimal within a logarithmic factor.
引用
收藏
页码：8728 / 8740
页数：13
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