Bias correction in multivariate extremes

Anne-Laure Fougères (1) , Laurens de Haan (2) , Cécile Mercadier (1)

1 PSPM - Probabilités, statistique, physique mathématique
2 Department of Economics, Faculty of Economics, Erasmus University Rotterdam

The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of ob- servations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this paper under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbi- ased versions of the empirical estimator introduced by Huang (1992). Since the new estimators have a regular behaviour with respect to the number of observations, it is possible to deduce aggregated ver- sions so that the choice of the threshold is substantially simplified. An extensive simulation study is provided as well as an application on real data.

Mots clés: Multivariate extreme value theory; bias correction; threshold choice; tail dependence

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

Anne-Laure Fougères, Laurens de Haan, Cécile Mercadier. Bias correction in multivariate extremes. Annals of Statistics, 2015, 43 (2), pp.903-934. ⟨hal-00942494v2⟩