On kernel smoothing for extremal quantile regression

By Abdelaati Daouia, Laurent Gardes, Stéphane Girard. 2012

149 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b3b4e5f168281500791f8e9d33cb2aa5f9bbc36e

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Citations in the corpus

Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions (2014, background): “˛njx/ is the extreme conditional quantile of level ˛n 2 .0; 1/ (for instance, Beirlant et al., 2004; Daouia et al., 2011, 2013; Gardes & Girard, 2010, 2012; Wang et al., 2012).”
Nonparametric regression estimation of conditional tails: the random covariate case (2014, unknown): “Thus, we have established (11), with δ′ = (δ1, δ2), and, by the Cramér-Wold device, also (10).”
Extreme M-quantiles as risk measures: From $L^{1}$ to $L^{p}$ optimization (2019, background): “p τ 1 npp,αn;2q ppq in (17) does not bring Monte Carlo evidence of any added value with respect to the benchmark estimators p q αnp2q and r q W αnp2q.”