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On kernel smoothing for extremal quantile regression

Abdelaati Daouia 1 Laurent Gardes 2 Stéphane Girard 3
3 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
Abstract : Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from the tails of the conditional distribution. The purpose of this paper is to extend their asymptotic theory far enough into the tails. We focus on extremal quantile regression estimators of a response variable given a vector of covariates in the general setting, whether the conditional extreme-value index is positive, negative, or zero. Specifically, we elucidate their limit distributions when they are located in the range of the data or near and even beyond the sample boundary, under technical conditions that link the speed of convergence of their (intermediate or extreme) order with the oscillations of the quantile function and a von-Mises property of the conditional distribution. A simulation experiment and an illustration on real data were proposed. The real data are the American electric data where the estimation of conditional extremes is found to be of genuine interest.
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Submitted on : Monday, July 9, 2012 - 9:13:02 AM
Last modification on : Tuesday, October 19, 2021 - 11:13:05 PM
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Abdelaati Daouia, Laurent Gardes, Stéphane Girard. On kernel smoothing for extremal quantile regression. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2013, 19 (5B), pp.2557-2589. ⟨10.3150/12-BEJ466⟩. ⟨hal-00630726v3⟩

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