Autin, F.
[]
Freyermuth, Jean-Marc
[UCL]
von Sachs, Rainer
[UCL]
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.
Bibliographic reference |
Autin, F. ; Freyermuth, Jean-Marc ; von Sachs, Rainer. Ideal denoising within a family of tree-structured wavelet estimators. ISBA Discussion Paper ; 1102 (2011) 24 pages |
Permanent URL |
http://hdl.handle.net/2078.1/91202 |