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The empirical distribution function for dependent variables:asymptotic and nonasymptotic results in ${\mathbb L}^p$
Jérôme Dedecker, Florence Merlevède
Journal:

ESAIM: Probability and Statistics / Volume 11 / June 2007

Published online by Cambridge University Press:

31 March 2007, pp. 102-114

Print publication:

June 2007
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Considering the centered empirical distribution function F n-F asa variable in ${\mathbb L}^p(\mu)$ , we derive non asymptotic upperbounds for the deviation of the ${\mathbb L}^p(\mu)$ -norms ofF n-F as well as central limit theorems for the empirical processindexed by the elements of generalized Sobolev balls. These resultsare valid for a large class of dependent sequences, includingnon-mixing processes and some dynamical systems.