Electronic Journal of Statistics

Functional kernel estimators of large conditional quantiles

Laurent Gardes and Stéphane Girard

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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.

Article information

Electron. J. Statist., Volume 6 (2012), 1715-1744.

First available in Project Euclid: 26 September 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G32: Statistics of extreme values; tail inference 62G30: Order statistics; empirical distribution functions
Secondary: 62E20: Asymptotic distribution theory

Conditional quantiles heavy-tailed distributions functional kernel estimator extreme-value theory


Gardes, Laurent; Girard, Stéphane. Functional kernel estimators of large conditional quantiles. Electron. J. Statist. 6 (2012), 1715--1744. doi:10.1214/12-EJS727. https://projecteuclid.org/euclid.ejs/1348665233

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