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arXiv · 1703.01654

Une alternative robuste au maximum de vraisemblance: la $ρ$-estimation

Yannick Baraud·Lucien Birgé
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Abstract

This paper is based on our personal notes for the short course we gave on January 5, 2017 at Institut Henri Poincaré, after an invitation of the SFdS. Our purpose is to give an overview of the method of $ρ$-estimation and of the optimality and robustness properties of the estimators built according to this procedure. This method can be viewed as the sequel of a long series of researches which were devoted to the construction of estimators with good properties in various statistical frameworks. We shall emphasize the connection between the $ρ$-estimators and the previous ones, in particular the maximum likelihood estimator, and we shall show, via some typical examples, that the $ρ$-estimators perform better from various points of view. ------ Cet article est fondé sur les notes du mini-cours que nous avons donné le 5 janvier 2017 à l'Institut Henri Poincaré à l'occasion d'une journée organisée par la SFdS et consacrée à la Statistique Mathématique. Il vise à donner un aperçu de la méthode de $ρ$-estimation ainsi que des propriétés d'optimalité et de robustesse des estimateurs construits selon cette procédure. Cette méthode s'inscrit dans une longue lignée de recherches dont l'objectif a été de produire des estimateurs possédant de bonnes propriétés pour un ensemble de cadres statistiques aussi vaste que possible. Nous mettrons en lumière les liens forts qui existent entre les $ρ$-estimateurs et ces prédécesseurs, notamment les estimateurs du maximum de vraisemblance, mais montrerons également, au travers d'exemples choisis, que les $ρ$-estimateurs les surpassent sur bien des aspects.

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Yannick Baraud, Lucien Birgé. 2017-07-02. Une alternative robuste au maximum de vraisemblance: la $ρ$-estimation. https://arxiv.org/abs/1703.01654

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