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

Aboubacrène Ag Ahmad (1) , Hadji Deme (1) , Aliou Diop (1) , Stéphane Girard (2, 3) , Antoine Usseglio-Carleve (2, 3)

1 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
3 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension

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 dispersion 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 may benefit from the same rate of convergence as in the unconditional situation. Its finite sample properties are illustrated both on simulated and real tsunami data.

Mots clés: Regression and dispersion functions; Extreme conditional quantile; Tail-index; Semi-parametric estimation

Domaines: Statistiques [math.ST]

Aboubacrène Ag Ahmad, Hadji Deme, Aliou Diop, Stéphane Girard, Antoine Usseglio-Carleve. Estimation of extreme quantiles from heavy-tailed distributions in a location-dispersion regression model. Electronic Journal of Statistics , 2020, 14 (2), pp.4421--4456. ⟨10.1214/20-EJS1779⟩. ⟨hal-02486937v3⟩