Statistics Papers
Document Type
Journal Article
Date of this Version
2009
Publication Source
The Annals of Statistics
Volume
37
Issue
2
Start Page
569
Last Page
595
DOI
10.1214/07-AOS538
Abstract
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.
Keywords
adaptivity, Besov body, block thresholding, James–Stein estimator, nonparametric regression, Stein’s unbiased risk estimate, wavelets
Recommended Citation
Cai, T., & Zhou, H. H. (2009). A Data-Driven Block Thresholding Approach to Wavelet Estimation. The Annals of Statistics, 37 (2), 569-595. http://dx.doi.org/10.1214/07-AOS538
Date Posted: 27 November 2017
This document has been peer reviewed.