The Annals of Statistics

A data-driven block thresholding approach to wavelet estimation

T. Tony Cai and Harrison H. Zhou

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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.

Article information

Ann. Statist., Volume 37, Number 2 (2009), 569-595.

First available in Project Euclid: 10 March 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Adaptivity Besov body block thresholding James–Stein estimator nonparametric regression Stein’s unbiased risk estimate wavelets


Cai, T. Tony; Zhou, Harrison H. A data-driven block thresholding approach to wavelet estimation. Ann. Statist. 37 (2009), no. 2, 569--595. doi:10.1214/07-AOS538.

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