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Article Dans Une Revue Electronic Journal of Statistics Année : 2012

Functional kernel estimators of large conditional quantiles

Résumé

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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Dates et versions

hal-00608192 , version 1 (12-07-2011)
hal-00608192 , version 2 (20-01-2012)
hal-00608192 , version 3 (21-08-2012)
hal-00608192 , version 4 (25-04-2013)

Identifiants

Citer

Laurent Gardes, Stéphane Girard. Functional kernel estimators of large conditional quantiles. Electronic Journal of Statistics , 2012, 6, pp.1715-1744. ⟨10.1214/12-EJS727⟩. ⟨hal-00608192v4⟩
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