Estimating extreme quantiles under random truncation

Laurent Gardes (1) , Gilles Stupfler (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 CERGAM - Centre d'Études et de Recherche en Gestion 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 the data is right-truncated. The weak consistency and asymptotic normality of the estimators are established and we illustrate the finite sample performance of our estimators on a simulation study.

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

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

Laurent Gardes, Gilles Stupfler. Estimating extreme quantiles under random truncation. 2014. ⟨hal-00942134v1⟩