Estimation of the conditional tail index using a smoothed local Hill estimator

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

For heavy-tailed distributions, the so-called tail index is an important parameter that controls the behavior of the tail distribution and is thus of primary interest to estimate extreme quantiles. In this paper, the estimation of the tail index is considered in the presence of a finite-dimensional random covariate. Uniform weak consistency and asymptotic normality of the proposed estimator are established and some illustrations on simulations are provided.

Mots clés: pointwise asymptotic normality; Heavy-tailed distribution; random covariate; uniform consistency; pointwise asymptotic normality.

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

Laurent Gardes, Gilles Stupfler. Estimation of the conditional tail index using a smoothed local Hill estimator. Extremes, 2014, 17 (1), pp.45-75. ⟨hal-00739454v2⟩