Geodesic
The empirical distribution function for dependent variables : asymptotic and nonasymptotic results in 𝕃 p
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 102-114

Voir la notice de l'article provenant de la source Numdam

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

DOI : 10.1051/ps:2007009
Classification : 60F10, 62G30
Keywords: deviation inequalities, weak dependence, Cramér-von Mises statistics, empirical process, expanding maps 
@article{PS_2007__11__102_0,
     author = {Dedecker, J\'er\^ome and Merlev\`ede, Florence},
     title = {The empirical distribution function for dependent variables : asymptotic and nonasymptotic results in ${\mathbb {L}}^p$},
     journal = {ESAIM: Probability and Statistics},
     pages = {102--114},
     publisher = {EDP-Sciences},
     volume = {11},
     year = {2007},
     doi = {10.1051/ps:2007009},
     mrnumber = {2299650},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007009/}
}
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
PY  - 2007
SP  - 102
EP  - 114
VL  - 11
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps:2007009/
DO  - 10.1051/ps:2007009
LA  - en
ID  - PS_2007__11__102_0
ER  - 
%0 Journal Article
%A Dedecker, Jérôme
%A Merlevède, Florence
%T The empirical distribution function for dependent variables : asymptotic and nonasymptotic results in ${\mathbb {L}}^p$
%J ESAIM: Probability and Statistics
%D 2007
%P 102-114
%V 11
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps:2007009/
%R 10.1051/ps:2007009
%G en
%F PS_2007__11__102_0
Dedecker, Jérôme; Merlevède, Florence. The empirical distribution function for dependent variables : asymptotic and nonasymptotic results in ${\mathbb {L}}^p$. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 102-114. doi: 10.1051/ps:2007009

Cité par Sources :