## Electronic Journal of Statistics

### Functional kernel estimators of large conditional quantiles

#### 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

https://projecteuclid.org/euclid.ejs/1348665233

Digital Object Identifier
doi:10.1214/12-EJS727

Mathematical Reviews number (MathSciNet)
MR2988462

Zentralblatt MATH identifier
1295.62052

#### 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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