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

Dedecker, Jérôme; Merlevède, Florence

doi:10.1051/ps:2007009

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

𝕃^{p}

Dedecker, Jérôme ; Merlevède, Florence

ESAIM: Probability and Statistics, Tome 11 (2007), pp. 102-114

Résumé

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.

MR

DOI : 10.1051/ps:2007009

Classification : 60F10, 62G30
Keywords: deviation inequalities, weak dependence, Cramér-von Mises statistics, empirical process, expanding maps

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     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},
     year = {2007},
     publisher = {EDP Sciences},
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     doi = {10.1051/ps:2007009},
     mrnumber = {2299650},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps:2007009/}
}

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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

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