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ELSEVIER Computational Statistics & Data Analysis22 (1996)351-361 COMPUTATIONAL
 

Summary: ELSEVIER Computational Statistics & Data Analysis22 (1996)351-361
COMPUTATIONAL
STATISTICS
&DATAANALYSIS
Adaptive thresholding of wavelet
coefficients
Felix Abramovich 1'*, Yoav Benjamini
Department of Statistics and OperationsResearch, TelAviv University,Ramat Aviv 69978, Israel
ReceivedAugust 1994;revised October 1995
Abstract
Wavelet techniques have become an attractive and efficient tool in function estimation. Given noisy
data, its discrete wavelet transform is an estimator of the wavelet coefficients. It has been shown by
Donoho and Johnstone (Biometrika 81 (1994) 425-455) that thresholding the estimated coefficients
and then reconstructing an estimated function reduces the expected risk close to the possible
minimum. They offered a global threshold 2 ~ a21~/~ for j >Jo, while the coefficients of the first
coarse jo levels are always included.
We demonstrate that the choice ofjo may strongly affect the corresponding estimators. Then, we
use the connection between thresholding and hypotheses testing to construct a thresholding proced-
ure based on the false discovery rate (FDR) approach to multiple testing of Benjamini and Hochberg
(J. Roy. Statist. Soc. Set. B 57 (1995) 289-300). The suggested procedure controls the expected

  

Source: Abramovich, Felix - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics