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Estimation non paramétrique pour des modèles de diffusion et de régression

Abstract : We consider the problem of estimating an unknown function at a fixed point in nonparametric regression or diffusion models. The risk associated to the use of an estimator is defined through the absolute error loss. In this work we aim at finding an asymptotic lower bound for the minimax risk and then to construct an asymptotically efficient estimator, that is to say an estimator for which the maximal risk asymptotically attains this bound.
For a nonparametric heteroscedastic model where the standard deviation of the noise depends on the regressor and on the regression function belonging to a weak hölderian class with known smoothness, we show that a kernel estimator is asymptotically efficient. When the smoothness of the regression function remains unknown, we obtain the adaptive rate of convergence of the estimators over a family of hölderian classes. Eventually for a diffusion model where the drift function belongs to a hölderian neighborhood of a lipschitzian function, we develop the construction of an asymptotically efficient kernel estimator.
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https://tel.archives-ouvertes.fr/tel-00338286
Contributor : Jean-Yves Brua <>
Submitted on : Wednesday, November 12, 2008 - 3:19:10 PM
Last modification on : Friday, June 19, 2020 - 9:10:04 AM
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Jean-Yves Brua. Estimation non paramétrique pour des modèles de diffusion et de régression. Mathématiques [math]. Université Louis Pasteur - Strasbourg I, 2008. Français. ⟨NNT : 2008STR13104⟩. ⟨tel-00338286⟩

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