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

Jérôme Dedecker; Florence Merlevède

ESAIM: Probability and Statistics (2007)

  • Volume: 11, page 102-114
  • ISSN: 1292-8100

Abstract

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Considering the centered empirical distribution function Fn-F as a variable in 𝕃 p ( μ ) , we derive non asymptotic upper bounds for the deviation of the 𝕃 p ( μ ) -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.

How to cite

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Dedecker, Jérôme, and Merlevède, Florence. "The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in ${\mathbb L}^p$." ESAIM: Probability and Statistics 11 (2007): 102-114. <http://eudml.org/doc/250088>.

@article{Dedecker2007,
abstract = { Considering the centered empirical distribution function Fn-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 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. },
author = {Dedecker, Jérôme, Merlevède, Florence},
journal = {ESAIM: Probability and Statistics},
keywords = {Deviation inequalities; weak dependence; Cramér-von Mises statistics; empirical process; expanding maps.; deviation inequalities; expanding maps},
language = {eng},
month = {3},
pages = {102-114},
publisher = {EDP Sciences},
title = {The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in $\{\mathbb L\}^p$},
url = {http://eudml.org/doc/250088},
volume = {11},
year = {2007},
}

TY - JOUR
AU - Dedecker, Jérôme
AU - Merlevède, Florence
TI - The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in ${\mathbb L}^p$
JO - ESAIM: Probability and Statistics
DA - 2007/3//
PB - EDP Sciences
VL - 11
SP - 102
EP - 114
AB - Considering the centered empirical distribution function Fn-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 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.
LA - eng
KW - Deviation inequalities; weak dependence; Cramér-von Mises statistics; empirical process; expanding maps.; deviation inequalities; expanding maps
UR - http://eudml.org/doc/250088
ER -

References

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