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The empirical distribution function for dependent variables: asymptotic and non asymptotic results in L^p

Abstract : Considering the centered empirical distribution function F n-F as a variable in L^p(mu) , we derive non asymptotic upper bounds for the deviation of the 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.
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https://hal.archives-ouvertes.fr/hal-00686009
Contributor : Jérôme Dedecker <>
Submitted on : Friday, April 6, 2012 - 4:35:22 PM
Last modification on : Saturday, March 28, 2020 - 2:06:32 AM

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  • HAL Id : hal-00686009, version 1

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Jerome Dedecker, F. Merlevède. The empirical distribution function for dependent variables: asymptotic and non asymptotic results in L^p. ESAIM: Probability and Statistics, EDP Sciences, 2007, 11, pp.102-114. ⟨hal-00686009⟩

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