Sur l'estimation adaptative de fonctions anisotropes

Abstract : This thesis is devoted to the study of statistical problems of non parametrical estimation. A noisy multidimensionnal signal is observed (for example an image if the dimension is equal to two) and our goal is to reconstruct it \emph{as best as possible}.

In order to achieve this goal, we consider the well known theory of adaptation on a minimax sense : we want to construct a single estimator which achieves on each fuctionnal space of a given collection the "best possible rate".

We introduce a new criterion in order to chose an optimal family of normalizations. This criterion is more sophisticated than criteria given by Lepski (1991) and Tsybakov (1998) and well adapted to multidimensionnal case.

Then, we prove two results of adaptation with respect to different collections of anisotropic H
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Theses
Mathématiques [math]. Université de Provence - Aix-Marseille I, 2005. Français


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Submitted on : Tuesday, January 31, 2006 - 2:58:09 PM
Last modification on : Tuesday, January 31, 2006 - 3:07:25 PM
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Klutchnikoff Nicolas. Sur l'estimation adaptative de fonctions anisotropes. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2005. Français. <tel-00011504>

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