Estimating Bivariate Tail: a copula based approach

Elena Di Bernardino (1) , Véronique Maume-Deschamps (1) , Clémentine Prieur (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 MOISE - Modelling, Observations, Identification for Environmental Sciences

This paper deals with the problem of estimating the tail of a bivariate distribution function. To this end we develop a general extension of the POT (Peaks-Over-Threshold) method, mainly based on a two-dimensional version of the Pickands-Balkema-de Haan Theorem. We introduce a new parameter that describes the nature of the tail dependence and we provide a way to estimate it. We construct a two-dimensional tail estimator and study its asymptotic properties. We also present real data examples which illustrate our theoretical results.

Mots clés: Extreme Value Theory; Peaks Over Threshold method; Pickands-Balkema-de Haan Theorem; Tail dependence

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

Elena Di Bernardino, Véronique Maume-Deschamps, Clémentine Prieur. Estimating Bivariate Tail: a copula based approach. Journal of Multivariate Analysis, 2013, 119, pp.81-100. ⟨10.1016/j.jmva.2013.03.020⟩. ⟨hal-00475386v3⟩