Quelques propriétés asymptotiques en estimation non paramétrique de fonctionnelles de processus stationnaires en temps continu

Abstract : The work of this thesis focuses upon some nonparametric estimation problems. More precisely, considering kernel estimators of the density, the regression and the conditional mode functions associated to a stationary continuous-time process, we aim at establishing some asymptotic properties while taking a sufficiently general dependency framework for the data as to be easily used in practice. The present manuscript includes four parts. The first one gives the state of the art related to the field of our concern and identifies well our contribution as compared to the existing results in the literature. In the second part, we focus on the kernel density estimation. In a rather general dependency setting, where we use a martingale difference device and a technique based on a sequence of projections on -fields, we establish the almost sure pointwise and uniform consistencies with rates of our estimate. In the third part, similar asymptotic properties are established for the kernel estimator of the regression function. Here and below, the processes are assumed to be ergodic In the same spirit, we study in the fourth part, the kernel estimate of conditional mode function for which we establish consistency properties with rates of convergence. The proposed estimator may be viewed as an alternative in the prediction issues to the usual regression function.
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Sultana Didi. Quelques propriétés asymptotiques en estimation non paramétrique de fonctionnelles de processus stationnaires en temps continu. Statistiques [math.ST]. Université Pierre et Marie Curie - Paris VI, 2014. Français. ⟨NNT : 2014PA066191⟩. ⟨tel-01081619⟩

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