Estimating extreme quantiles under random truncation

Laurent Gardes (1) , Gilles Stupfler (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

The goal of this paper is to provide estimators of the tail index and extreme quantiles of a heavy-tailed random variable when it is right-truncated. The weak consistency and asymptotic normality of the estimators are established. The finite sample performance of our estimators is illustrated on a simulation study and we showcase our estimators on a real set of failure data..

Mots clés: Heavy-tailed distribution; tail index; extreme quantile; consistency; asymptotic normality; Heavy-tailed distribution

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

Laurent Gardes, Gilles Stupfler. Estimating extreme quantiles under random truncation. Test, 2015, 24 (2), pp.207-227. ⟨10.1007/s11749-014-0403-5⟩. ⟨hal-00942134v2⟩