Docteur en statistique, INRIA Grenoble, Projet Mistis |
Safari, Firefox, Chrome et Opera 
|
Abstract - We address the estimation of extreme level curves of heavy-tailed distributions. This problem is equivalent to estimating quantiles when covariate information is available and in the case where their order converges to one as the sample size increases. We show that, under some conditions, these so-called "extreme conditional quantiles" can still be estimated through a kernel estimator of the conditional survival function. Sufficient conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed estimators. These results are illustrated both on simulated and real datasets.
,
Abstract - Nous proposons dans le cas des distributions à queue lourde une méthode d'estimation des quantiles extrêmes en présence d'une covariable. La loi limite d'un tel estimateur est ensuite donnée en fonction de la vitesse de convergence de l'ordre du quantile vers un. Pour conclure, une illustration sur données simulées est présentée.
Abstract - We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme" quantiles can be located in the range of the data or near and even beyond the boundary of the sample, depending on the convergence rate of their order to one. Nonparametric estimators of these functional extreme quantiles are introduced, their asymptotic distributions are established and an illustration on a real data set is presented.  |
|
|
|
