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| HAL : hal-00608192, version 4 |
| arXiv : 1107.2261 |
| Fiche détaillée |  Récupérer au format |
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| Electronic Journal of Statistics 6 (2012) 1715-1744 |
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| Versions disponibles : | v1 (12-07-2011) | v2 (20-01-2012) | v3 (21-08-2012) | v4 (25-04-2013) |
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| Functional kernel estimators of large conditional quantiles |
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| Laurent Gardes 1Stéphane Girard 2 |
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| (2012) |
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| We address the estimation of conditional quantiles when the covariate is functional and when the order of the quantiles converges to one as the sample size increases. In a first time, we investigate to what extent these large conditional quantiles can still be estimated through a functional 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. In a second time, basing on these result, a functional Weissman estimator is derived, permitting to estimate large conditional quantiles of arbitrary large order. These results are illustrated on finite sample situations. |
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| 1 : | Institut de Recherche Mathématique Avancée (IRMA) |
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CNRS : UMR7501 – Université de Strasbourg |
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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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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Conditional quantiles – heavy-tailed distributions – functional kernel estimator – extreme-value theory |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00608192, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00608192 | |
| oai:hal.archives-ouvertes.fr:hal-00608192 | |
| Contributeur : Laurent Gardes | |
| Soumis le : Jeudi 25 Avril 2013, 11:58:54 | |
| Dernière modification le : Jeudi 25 Avril 2013, 21:52:37 | |
