文章基本信息

标题：Functional kernel estimators of large conditional quantiles
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作者：Laurent Gardes ; Stéphane Girard
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2012
卷号：6
页码：1715-1744
DOI：10.1214/12-EJS727
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.