Functional nonparametric estimation of conditional extreme quantiles

Authors:
Laurent Gardes;Stéphane Girard;Alexandre Lekina
Affiliations:
Team Mistis, INRIA Rhône-Alpes and LJK, 655, avenue de l'Europe, Montbonnot 38334 Saint-Ismier cedex, France;Team Mistis, INRIA Rhône-Alpes and LJK, 655, avenue de l'Europe, Montbonnot 38334 Saint-Ismier cedex, France;Team Mistis, INRIA Rhône-Alpes and LJK, 655, avenue de l'Europe, Montbonnot 38334 Saint-Ismier cedex, France
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such ''extreme'' quantiles can be located in the range of the data or near and even beyond the boundary of the sample, depending on the convergence rate of their order to one. Nonparametric estimators of these functional extreme quantiles are introduced, their asymptotic distributions are established and their finite sample behavior is investigated.