Estimation non paramétrique pour les modèles autorégressifs

Abstract : This thesis is devoted to nonparametric estimation for autoregressive models. We consider the problem of estimating an unknown function at a fixed point using data governed by autoregressive models. To define the risk associated with the use of an estimator and thus measure the quality of it, we use the loss function related to the absolute error. The work of this thesis follows the minimax approach for which the goal is to find a lower bound of the asymptotic minimax risk and then to construct an estimator, said asymptotically efficient, for which the maximum risk reaches asymptotically this bound. For a nonparametric autoregressive model where the autoregressive function is supposed to belong to a weak H\"{o}lder class with known regularity, we show that a kernel estimator is asymptotically efficient. When the regularity of the autoregressive function is unknown, we get the minimax adaptive convergence rate of estimators on a family of H\"{o}lderian classes.\\
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Mathématiques [math]. Université de Rouen, 2009. Français
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  • HAL Id : tel-00464024, version 1



Ouerdia Arkoun. Estimation non paramétrique pour les modèles autorégressifs. Mathématiques [math]. Université de Rouen, 2009. Français. 〈tel-00464024〉



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