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Lois limites fonctionnelles pour le processus empirique et applications

Abstract : In this thesis, we are concerned with nonparametric estimation of the density given a random sample. We establish asymptotic properties of density estimators by deducing them from functional limit laws for the local empirical process in a general context. The thesis is divided in two main parts, we describe as follows. The first part is devoted to local functional limit laws which are established for three sets of sequences of random functions, built from: the uniform empirical process, the uniform quantiles process and from the Kaplan-Meier empirical process. The functional laws are uniform relative to the increments size of the local empirical processes and describe the asymptotic behavior of the Hausdorff set-distance between each one of the three sets and a Strassen-type set. The purpose of the second part is nonparametric density estimation. We present several statistical applications of the previous functional limit laws, which consist on limit laws describing the asymptotic behavior of nonparametric density estimators, such as kernel estimators, the nearest-neighbor estimator, and kernel estimators of lifetime density and failure rate in a right censorship model. These applications are new sharp uniform-in-bandwidth limit laws for the last estimators in the framework of convergence in probability.
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Submitted on : Wednesday, December 19, 2012 - 9:50:49 AM
Last modification on : Wednesday, January 26, 2022 - 3:42:01 AM
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  • HAL Id : tel-00766805, version 1


Sarah Ouadah. Lois limites fonctionnelles pour le processus empirique et applications. Statistiques [math.ST]. Université Pierre et Marie Curie - Paris VI, 2012. Français. ⟨tel-00766805⟩



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