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On the strong consistency of the kernel estimator of extreme conditional quantiles

Stéphane Girard 1, * Sana Louhichi 2
* Corresponding author
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
2 IPS - Inférence Processus Stochastiques
LJK - Laboratoire Jean Kuntzmann
Abstract : Nonparametric regression quantiles can be obtained by inverting a kernel estimator of the conditional distribution. The asymptotic properties of this estimator are well-known in the case of ordinary quantiles of fixed order. The goal of this paper is to establish the strong consistency of the estimator in case of extreme conditional quantiles. In such a case, the probability of exceeding the quantile tends to zero as the sample size increases, and the extreme conditional quantile is thus located in the distribution tails.
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Stéphane Girard, Sana Louhichi. On the strong consistency of the kernel estimator of extreme conditional quantiles. Elias Ould Said. Functional Statistics and Applications, Springer, pp.59--77, 2015, Contributions to Statistics, 978-3-319-22475-6. ⟨10.1007/978-3-319-22476-3_4⟩. ⟨hal-00956351v2⟩



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