Estimation of extreme quantiles of heavy-tailed distributions in a location-dispersion regression model

Aboubacrène Ag (1) , Hadji Deme (1) , Aliou Diop (1) , Stéphane Girard (2) , Antoine Usseglio-Carleve (2)

1 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

We consider a location-dispersion regression model for heavy-tailed distributions when the multidimensional covariate is deterministic. In a first step, nonparametric estimators of the regression and precision functions are introduced. This permits, in a second step, to derive an estimator of the conditional extreme-value index computed on the residuals. Finally, a plug-in estimator of extreme conditional quantiles is built using these two preliminary steps. It is shown that the resulting semi-parametric estimator is asymptotically Gaussian and benefits from the same rate of convergence as in the unconditional situation. Its finite sample properties are illustrated both on simulated and real data.

Keywords: Semi-parametric estimation; tail-index; extreme conditional quantile; regression and dispersion functions

Domains: Statistics [math.ST]

Aboubacrène Ag, Hadji Deme, Aliou Diop, Stéphane Girard, Antoine Usseglio-Carleve. Estimation of extreme quantiles of heavy-tailed distributions in a location-dispersion regression model. 2020. ⟨hal-02486937v1⟩