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2012 Functional kernel estimators of large conditional quantiles
Laurent Gardes, Stéphane Girard
Electron. J. Statist. 6: 1715-1744 (2012). DOI: 10.1214/12-EJS727

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.

Citation

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Laurent Gardes. Stéphane Girard. "Functional kernel estimators of large conditional quantiles." Electron. J. Statist. 6 1715 - 1744, 2012. https://doi.org/10.1214/12-EJS727

Information

Published: 2012
First available in Project Euclid: 26 September 2012

zbMATH: 1295.62052
MathSciNet: MR2988462
Digital Object Identifier: 10.1214/12-EJS727

Subjects:
Primary: 62G30, 62G32
Secondary: 62E20

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
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