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Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes.

Abstract : This thesis deals with the central limit theorem for dependent random fields and its applications to nonparametric statistics. In the first part, we establish some quenched central limit theorems for random fields satisfying a projective condition à la Hannan (1973). Functional versions of these theorems are also considered. In the second part, we prove the asymptotic normality of kernel density and regression estimators for strongly mixing random fields in the sense of Rosenblatt (1956) and for weakly dependent random fields in the sense of Wu (2005). First, we establish the result for the kernel regression estimator introduced by Elizbar Nadaraya (1964) and Geoffrey Watson (1964). Then, we extend these results to a large class of recursive estimators defined by Peter Hall and Prakash Patil (1994).
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Submitted on : Tuesday, February 2, 2021 - 12:57:08 PM
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Lucas Reding. Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes.. Mathématiques générales [math.GM]. Normandie Université, 2020. Français. ⟨NNT : 2020NORMR049⟩. ⟨tel-03128648⟩

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