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We address the estimation of conditional quantiles when the covariate isfunctional and when the order of the quantiles converges to one as the samplesize increases. In a first time, we investigate to what extent these largeconditional quantiles can still be estimated through a functional kernelestimator of the conditional survival function. Sufficient conditions on therate of convergence of their order to one are provided to obtain asymptoticallyGaussian distributed estimators. In a second time, basing on these result, afunctional Weissman estimator is derived, permitting to estimate largeconditional quantiles of arbitrary large order. These results are illustratedon finite sample situations.

Functional kernel estimators of large conditional quantiles