| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 102 - 114 | |
| DOI | https://doi.org/10.1051/ps:2007009 | |
| Published online | 31 March 2007 | |
The empirical distribution function for dependent variables:
asymptotic and nonasymptotic results in 
1
Laboratoire de Statistique Théorique et Appliquée, Université
Paris 6, 175 rue du Chevaleret, 75013 Paris, France; dedecker@ccr.jussieu.fr
2
Laboratoire de probabilités
et modèles aléatoires, UMR 7599,
Université
Paris 6, 175 rue du Chevaleret, 75013 Paris, France; merleve@ccr.jussieu.fr
Received:
20
September
2005
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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