# Kernel estimators of extreme level curves

2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We address the estimation of extreme level curves of heavy-tailed distributions. This problem is equivalent to estimating quantiles when covariate information is available and when their order converges to one as the sample size increases. We show that, under some conditions, these so-called extreme conditional quantiles'' can still be estimated through a 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. Making use of this result, some kernel estimators of the conditional tail-index are introduced and a Weissman type estimator is derived, permitting to estimate extreme conditional quantiles of arbitrary large order. These results are illustrated through simulated and real datasets.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/inria-00393588
Contributor : Stephane Girard <>
Submitted on : Friday, November 20, 2009 - 11:09:31 AM
Last modification on : Monday, April 9, 2018 - 12:22:26 PM
Long-term archiving on : Thursday, September 23, 2010 - 10:51:50 AM

### File

qda2.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : inria-00393588, version 2

### Citation

Abdelaati Daouia, Laurent Gardes, Stéphane Girard, Alexandre Lekina. Kernel estimators of extreme level curves. 2009. ⟨inria-00393588v2⟩

Record views