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Quelques contributions à l'estimation fonctionnelle par méthodes d'ondelettes

Abstract : We present some contributions to the nonparametric functional estimation via wavelet methods.
Our study is divided in two parts. The first part is devoted to the study of complex statistical models. More precisely, we consider a generalized white noise model and the regression model with random design.
Each of them has a function disturbing the estimate of the unknown function. Our aim is to identify the exact influence of this parasitic function via the minimax approach under the Lp risk. Firtsly, we use conventional wavelet methods to determine the limits of this approach when the unknown function is supposed to belong to Besov balls. Secondly, we study the alternative of the weighted Besov balls and the warped wavelet bases. The second part is devoted to the adaptive estimation. In particular, we study the performances of several wavelet block thresholding estimators under the Lp risk.
We show that they enjoy excellent minimax and maxiset properties for numerous statistical models.
The regression model with random design and a deconvolution problem are considered.
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https://tel.archives-ouvertes.fr/tel-00121364
Contributor : Christophe Chesneau <>
Submitted on : Wednesday, December 20, 2006 - 1:45:32 PM
Last modification on : Wednesday, December 9, 2020 - 3:14:34 PM
Long-term archiving on: : Thursday, September 20, 2012 - 4:25:44 PM

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  • HAL Id : tel-00121364, version 1

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Christophe Chesneau. Quelques contributions à l'estimation fonctionnelle par méthodes d'ondelettes. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2006. Français. ⟨tel-00121364⟩

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