# The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in ${\mathbb{L}}^{p}$

Jérôme Dedecker; Florence Merlevède

ESAIM: Probability and Statistics (2007)

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

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topDedecker, 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 -

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