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Functional nonparametric estimation of conditional extreme quantiles

Laurent Gardes 1 Stéphane Girard 1 Alexandre Lekina 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
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.
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Laurent Gardes, Stéphane Girard, Alexandre Lekina. Functional nonparametric estimation of conditional extreme quantiles. Journal of Multivariate Analysis, Elsevier, 2010, 101 (2), pp.419-433. ⟨10.1016/j.jmva.2009.06.007⟩. ⟨hal-00289996v4⟩

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