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Habilitation à diriger des recherches

Dépendance faible: estimation et théorèmes limite.
Application à l'étude statistique de certains systèmes dynamiques.

Abstract : The major part of the presented work is devoted to new concepts of dependence
extending and generalizing the classical concepts of mixing of a stationary sequence. These
concepts allow the statement of various inequalities and limit theorems for different classes of
processes such as dynamical systems, non irreducible Markov chains, or Bernoulli shifts. These
results are then applied to derive various applications in the field of non parametric statistic.
Two other fields are also studied in the present manuscript : on one hand the study of large
deviation principles (in particular for generalized records for triangular arrays of exchangeable
variables), and the other hand the problem of adaptive estimation of linear functionals by
Gaussian model selection.
Document type :
Habilitation à diriger des recherches
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Contributor : Clémentine Prieur <>
Submitted on : Monday, February 26, 2007 - 2:40:59 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
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Clémentine Prieur. Dépendance faible: estimation et théorèmes limite.
Application à l'étude statistique de certains systèmes dynamiques.. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2006. ⟨tel-00133468⟩

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