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Quelques Problèmes de Statistique autour des processus de Poisson

Abstract : The main purpose of this thesis is to develop statistical methodologies for stochastic processes data and more precisely Cox process data.The problems considered arise from three different contexts: nonparametric tests, nonparametric kernel estimation and minimax estimation.We first study the statistical test problem of detecting wether a Cox process is Poisson or not.Then, we introduce a semiparametric estimate of the regression over a Poisson point process. Using Itô’s famous chaos expansion for Poisson functionals, we derive asymptotic minimax properties of our estimator.Finally, we introduce a nonparametric estimate of the intensity of a Cox process whenever it is a deterministic function of a known coprocess.
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Submitted on : Thursday, September 21, 2017 - 10:41:06 AM
Last modification on : Friday, May 20, 2022 - 9:04:49 AM


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  • HAL Id : tel-01591254, version 1


Gaspar Massiot. Quelques Problèmes de Statistique autour des processus de Poisson. Statistiques [math.ST]. École normale supérieure de Rennes, 2017. Français. ⟨NNT : 2017ENSR0006⟩. ⟨tel-01591254⟩



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