On the estimation of the functional Weibull tail-coefficient

Laurent Gardes (1) , Stéphane Girard (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

We present a nonparametric family of estimators for the tail index of a Weibull tail-distribution when functional covariate is available. Our estimators are based on a kernel estimator of extreme conditional quantiles. Asymptotic normality of the estimators is proved under mild regularity conditions. Their finite sample performances are illustrated both on simulated and real data.

Mots clés: Conditional Weibull tail-coefficient; nonparametric estimation; extreme quantiles

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Laurent Gardes, Stéphane Girard. On the estimation of the functional Weibull tail-coefficient. Journal of Multivariate Analysis, 2016, Special Issue on Statistical Models and Methods for High or Infinite Dimensional Spaces, 146 (C), pp.29--45. ⟨10.1016/j.jmva.2015.05.007⟩. ⟨hal-01063569v3⟩