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Please use this identifier to cite or link to this item : http://hdl.handle.net/2078.1/91202
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.
|Publication Date :||2011|
|Document type :||Document de travail (Working Paper)|
|Number of pages :||24 page(s)|
|Collection :||ISBA Discussion Paper - 1102|
|Subject :||Besov spaces ; CART ; Maxiset and oracle approaches ; Rate ; Wavelet-based estimation|