Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||102 - 114|
|Published online||31 March 2007|
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in
Laboratoire de Statistique Théorique et Appliquée, Université
Paris 6, 175 rue du Chevaleret, 75013 Paris, France; firstname.lastname@example.org
2 Laboratoire de probabilités et modèles aléatoires, UMR 7599, Université Paris 6, 175 rue du Chevaleret, 75013 Paris, France; email@example.com
Revised: 22 May 2006
Considering the centered empirical distribution function Fn-F as a variable in , we derive non asymptotic upper bounds for the deviation of the -norms of Fn-F as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.
Mathematics Subject Classification: 60F10 / 62G30
Key words: Deviation inequalities / weak dependence / Cramér-von Mises statistics / empirical process / expanding maps.
© EDP Sciences, SMAI, 2007
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