Open Access
2011 Ideal denoising within a family of tree-structured wavelet estimators
Florent Autin, Jean-Marc Freyermuth, Rainer von Sachs
Electron. J. Statist. 5: 829-855 (2011). DOI: 10.1214/11-EJS628


We focus on the performances of tree-structured wavelet estimators belonging to a large family of keep-or-kill rules, namely the Vertical Block Thresholding family. For each estimator, we provide the maximal functional space (maxiset) for which the quadratic risk reaches a given rate of convergence. Following a discussion on the maxiset embeddings, we identify the ideal estimator of this family, that is the one associated with the largest maxiset. We emphasize the importance of such a result since the ideal estimator is different from the usual (plug-in) estimator used to mimic the performances of the Oracle. Finally, we confirm the good performances of the ideal estimator compared to the other elements of that family through extensive numerical experiments.


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Florent Autin. Jean-Marc Freyermuth. Rainer von Sachs. "Ideal denoising within a family of tree-structured wavelet estimators." Electron. J. Statist. 5 829 - 855, 2011.


Published: 2011
First available in Project Euclid: 9 August 2011

zbMATH: 1274.62228
MathSciNet: MR2824818
Digital Object Identifier: 10.1214/11-EJS628

Primary: 41A25 , ‎42C40 , 62G05 , 62G20 , 65T60

Keywords: Besov spaces , CART , Curve estimation , maxiset and oracle approaches , rate of convergence , Thresholding methods , tree structure , wavelet estimators

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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