Electronic Journal of Statistics

Functional kernel estimators of large conditional quantiles

Laurent Gardes and Stéphane Girard

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 26 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1348665233

Digital Object Identifier
doi:10.1214/12-EJS727

Mathematical Reviews number (MathSciNet)
MR2988462

Zentralblatt MATH identifier
1295.62052

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

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

Citation

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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