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November 2013 On kernel smoothing for extremal quantile regression
Abdelaati Daouia, Laurent Gardes, Stéphane Girard
Bernoulli 19(5B): 2557-2589 (November 2013). DOI: 10.3150/12-BEJ466

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 presented. The real data are the American electric data where the estimation of conditional extremes is found to be of genuine interest.

Citation

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Abdelaati Daouia. Laurent Gardes. Stéphane Girard. "On kernel smoothing for extremal quantile regression." Bernoulli 19 (5B) 2557 - 2589, November 2013. https://doi.org/10.3150/12-BEJ466

Information

Published: November 2013
First available in Project Euclid: 3 December 2013

zbMATH: 1281.62097
MathSciNet: MR3160564
Digital Object Identifier: 10.3150/12-BEJ466

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 5B • November 2013
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