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April 2009 A data-driven block thresholding approach to wavelet estimation
T. Tony Cai, Harrison H. Zhou
Ann. Statist. 37(2): 569-595 (April 2009). DOI: 10.1214/07-AOS538


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.


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T. Tony Cai. Harrison H. Zhou. "A data-driven block thresholding approach to wavelet estimation." Ann. Statist. 37 (2) 569 - 595, April 2009.


Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62032
MathSciNet: MR2502643
Digital Object Identifier: 10.1214/07-AOS538

Primary: 62G08
Secondary: 62G20

Keywords: Adaptivity , Besov body , block thresholding , James–Stein estimator , Nonparametric regression , Stein’s unbiased risk estimate , Wavelets

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 2 • April 2009
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