Empirical Phi-discrepancies and quasi-empirical likelihood: exponential bounds
ESAIM. Proceedings, Tome 51 (2015), pp. 212-231
Cet article a éte moissonné depuis la source EDP Sciences
We review some recent extensions of the so-called generalized empirical likelihood method, when the Kullback distance is replaced by some general convex divergence. We propose to use, instead of empirical likelihood, some regularized form or quasi-empirical likelihood method, corresponding to a convex combination of Kullback and χ2 discrepancies. We show that for some adequate choice of the weight in this combination, the corresponding quasi-empirical likelihood is Bartlett-correctable. We also establish some non-asymptotic exponential bounds for the confidence regions obtained by using this method. These bounds are derived via bounds for self-normalized sums in the multivariate case obtained in a previous work by the authors. We also show that this kind of results may be extended to process valued infinite dimensional parameters. In this case some known results about self-normalized processes may be used to control the behavior of generalized empirical likelihood.
Affiliations des auteurs :
Patrice Bertail 1 ; Emmanuelle Gautherat 2 ; Hugo Harari-Kermadec 3
@article{EP_2015_51_a12,
author = {Patrice Bertail and Emmanuelle Gautherat and Hugo Harari-Kermadec},
title = {Empirical {Phi-discrepancies} and quasi-empirical likelihood: exponential bounds},
journal = {ESAIM. Proceedings},
pages = {212--231},
year = {2015},
volume = {51},
doi = {10.1051/proc/201551012},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201551012/}
}
TY - JOUR AU - Patrice Bertail AU - Emmanuelle Gautherat AU - Hugo Harari-Kermadec TI - Empirical Phi-discrepancies and quasi-empirical likelihood: exponential bounds JO - ESAIM. Proceedings PY - 2015 SP - 212 EP - 231 VL - 51 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201551012/ DO - 10.1051/proc/201551012 LA - en ID - EP_2015_51_a12 ER -
%0 Journal Article %A Patrice Bertail %A Emmanuelle Gautherat %A Hugo Harari-Kermadec %T Empirical Phi-discrepancies and quasi-empirical likelihood: exponential bounds %J ESAIM. Proceedings %D 2015 %P 212-231 %V 51 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201551012/ %R 10.1051/proc/201551012 %G en %F EP_2015_51_a12
Patrice Bertail; Emmanuelle Gautherat; Hugo Harari-Kermadec. Empirical Phi-discrepancies and quasi-empirical likelihood: exponential bounds. ESAIM. Proceedings, Tome 51 (2015), pp. 212-231. doi: 10.1051/proc/201551012
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