Ideal denoising within a family of tree-structured wavelet estimators
(2011) Electronic Journal of Statistics — Vol. 5, p. 829-855 (2011)
Files
106779.pdf
Open Access - Adobe PDF
- 442.39 KB
Details
- Authors
- Abstract
- 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.
- Affiliations
Université d’Aix-Marseille 1, France
Citations
Autin, F., Freyermuth, J.-M., & von Sachs, R. (2011). Ideal denoising within a family of tree-structured wavelet estimators. Electronic Journal of Statistics, 5, 829-855. https://doi.org/10.1214/11-EJS628 (Original work published 2011)