A DATA-DRIVEN BLOCK THRESHOLDING APPROACH TO WAVELET ESTIMATION

• 成果类型: Article
• 署名作者: Cai, T. Tony; Zhou, Harrison H.
• 署名单位: University of Pennsylvania; Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS538
• 发表日期: 2009
• 页码: 569-595
• 关键词: Minimax Risk; shrinkage; density

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.