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Choix optimal du paramètre de lissage dans l'estimation non paramétrique de la fonction de densité pour des processus stationnaires à temps continu

Abstract : The work this thesis focuses on the choice of the smoothing parameter in the context of non-parametric estimation of the density function for stationary ergodic continuous time processes. The accuracy of the estimation depends greatly on the choice of this parameter. The main goal of this work is to build an automatic window selection procedure and establish asymptotic properties while considering a general dependency framework that can be easily used in practice. The manuscript is divided into three parts. The first part reviews the literature on the subject, set the state of the art and discusses our contribution in within. In the second part, we design an automatical method for selecting the smoothing parameter when the density is estimated by the Kernel method. This choice stemming from the cross-validation method is asymptotically optimal. In the third part, we establish an asymptotic properties pertaining to consistency with rate for the resulting estimate of the window-width.
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https://tel.archives-ouvertes.fr/tel-02001263
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Khadijetou El Heda. Choix optimal du paramètre de lissage dans l'estimation non paramétrique de la fonction de densité pour des processus stationnaires à temps continu. Statistiques [math.ST]. Université du Littoral Côte d'Opale, 2018. Français. ⟨NNT : 2018DUNK0484⟩. ⟨tel-02001263⟩

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