Ideal denoising within a family of tree-structured wavelet estimators

Autin, F.;Freyermuth, Jean-Marc;von Sachs, Rainer
(2011) , 24 pages

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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 our theoretical results through extensive numerical experiments.
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Autin, F., Freyermuth, J.-M., & von Sachs, R. (2011). Ideal denoising within a family of tree-structured wavelet estimators (ISBA Discussion Paper 1102). https://hdl.handle.net/2078.5/210201