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Theses

Processus empirique avec informations auxiliaires

Abstract : This thesis deals with the study of the empirical process with auxiliary information, that is to say information that one would have a priori or that one would have obtained with a source of information. We show in this thesis how to modify the empirical process to take into account auxiliary information. We also show that providing auxiliary information at the empirical process level improves the quality of statistical estimates as well as the power of standard statistical tests. The first chapter contains the main definitions as well as the important results used in this thesis. In the second and third chapter, we study the particular case where the auxiliary information is respectively given by the probability of sets of one or more given partition(s). In particular, the third chapter focuses on the method of Raking-Ratio, a method widely used in statistics to combine the knowledge of the probability of sets of several partitions. In the fourth chapter, we generalize the definition of auxiliary information while retaining the possibility of establishing strong approximation results, at the cost of a loss of generalization. In the last chapter, we establish the strong approximation of the empirical process in the case of the bootstrap method and we combine the bootstrap method with that of the Raking-Ratio.
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Mickael Albertus. Processus empirique avec informations auxiliaires. Statistiques [math.ST]. Université Paul Sabatier - Toulouse III, 2019. Français. ⟨NNT : 2019TOU30095⟩. ⟨tel-02501305⟩

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