A DATA-DRIVEN BLOCK THRESHOLDING APPROACH TO WAVELET ESTIMATION

被引：57
|
作者：
Cai, T. Tony [1 ]
Zhou, Harrison H. [2 ]
机构：
[1] Univ Penn, Dept Stat, Wharton Sch, Philadelphia, PA 19104 USA
[2] Yale Univ, Dept Stat, New Haven, CT 06511 USA
来源：
ANNALS OF STATISTICS | 2009年 / 37卷 / 02期
基金：
美国国家科学基金会;
关键词：
Adaptivity; Besov body; block thresholding; James-Stein estimator; non-parametric regression; Stein's unbiased risk estimate; wavelets; MINIMAX RISK; SHRINKAGE; DENSITY;
D O I：
10.1214/07-AOS538
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：
A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein's unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov Bodies including both the "dense" and "sparse" cases. The procedure is easy to implement. Numerical results show that it has, superior finite sample performance in comparison to the other leading wavelet thresholding estimators.
引用
收藏
页码：569 / 595
页数：27
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