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Kernel estimators of extreme level curves

Abdelaati Daouia 1 Laurent Gardes 2 Stéphane Girard 2 Alexandre Lekina 2
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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.
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https://hal.inria.fr/inria-00393588
Contributor : Stephane Girard <>
Submitted on : Tuesday, June 9, 2009 - 3:48:10 PM
Last modification on : Wednesday, July 1, 2020 - 1:46:05 PM
Document(s) archivé(s) le : Friday, June 11, 2010 - 12:32:19 AM

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  • HAL Id : inria-00393588, version 1

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Abdelaati Daouia, Laurent Gardes, Stéphane Girard, Alexandre Lekina. Kernel estimators of extreme level curves. 2009. ⟨inria-00393588v1⟩

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