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Zbl 1184.60008
Dedecker, Jérôme; Merlevède, Florence
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in ${\mathbb L}^p$. (English)
[J] ESAIM, Probab. Stat. 11, 102-114 (2007). ISSN 1292-8100; ISSN 1262-3318/e

Summary: Considering the centered empirical distribution function $F_n-F$ as a variable in ${\mathbb L}^p(\mu)$, we derive non asymptotic upper bounds for the deviation of the ${\mathbb L}^p(\mu)$-norms of $F_n-F$ 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.

MSC 2000:: *60F10 Large deviations
62G30 Order statistics, etc.
60F05 Weak limit theorems

Keywords: deviation inequalities; weak dependence; Cramér-von Mises statistics; empirical process; expanding maps

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