2009/03/10 by T. Tony Cai, Harrison H. Zhou · 2 citations
Computer Science · Engineering · Mathematics · #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #math.ST #msc:62G08 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/07-aos538
published as Annals of Statistics 2009, Vol. 37, No. 2, 569-595 · Published in at http://dx.doi.org/10.1214/07-AOS538 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2009/03/10 · arxiv created 2009/03/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.