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| HAL: inria-00393588, version 3 |
| See detailed view |  BibTeX,EndNote,... |
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| Available versions | v1 (2009-06-09) | v2 (2009-11-20) | v3 (2010-05-06) |
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| Kernel estimators of extreme level curves |
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| Abdelaati Daouia 1Laurent Gardes 2 |
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| (2009-06-09) |
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| 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 when 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. Making use of this result, some kernel estimators of the conditional tail-index are introduced and a Weissman type estimator is derived, permitting to estimate extreme conditional quantiles of arbitrary large order. These results are illustrated through simulated and real datasets. |
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| 1: | Groupe de recherche en économie mathématique et quantitative (GREMAQ) |
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CNRS : UMR5604 – Université des Sciences Sociales - Toulouse I – École des Hautes Études en Sciences Sociales [EHESS] – Institut national de la recherche agronomique (INRA) : UMR |
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| 2: | MISTIS (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann) |
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INRIA – Laboratoire Jean Kuntzmann |
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| Domain | : | Mathematics/Statistics Statistics/Statistics Theory |
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| Conditional quantiles – Heavy-tail distributions – Kernel estimator – Extreme-values |
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| inria-00393588, version 3 | |
| http://hal.inria.fr/inria-00393588 | |
| oai:hal.inria.fr:inria-00393588 | |
| From: Stephane Girard | |
| Submitted on: Thursday, 6 May 2010 09:53:43 | |
| Updated on: Friday, 7 May 2010 08:52:52 | |
