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Functional kernel estimators of large conditional quantiles

Laurent Gardes 1 Stéphane Girard 2
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : 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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Laurent Gardes, Stéphane Girard. Functional kernel estimators of large conditional quantiles. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2012, 6, pp.1715-1744. ⟨10.1214/12-EJS727⟩. ⟨hal-00608192v4⟩



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