Inference for asymptotically independent samples of extremes

Armelle Guillou (1) , Simone A. Padoan (2) , Stefano Rizzelli (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Department of Decision Sciences, Bocconi University

An important topic of the multivariate extreme-value theory is to develop probabilistic models and statistical methods to describe and measure the strength of dependence among extreme observations. The theory is well established for data whose dependence structure is compatible with that of asymptotically dependent models. On the contrary, in many applications data do not comply with asymptotically dependent models and thus new tools are required. This article contributes to the methodological development of such a context, by considering a componentwise maxima approach. First we propose a statistical test based on the classical Pickands dependence function to verify whether asymptotic dependence or independence holds. Then, we present a new Pickands dependence function to describe the extremal dependence under asymptotic independence. Finally, we propose an estimator of the latter, we establish its main asymptotic properties and we illustrate its performance by a simulation study.

Mots clés: and phrases: Extremal dependence; extreme-value copula; nonparametric estimation; Pickands depen- dence function

Domaines: Statistiques [math.ST]

Armelle Guillou, Simone A. Padoan, Stefano Rizzelli. Inference for asymptotically independent samples of extremes. Journal of Multivariate Analysis, 2018, 167, pp.114-135. ⟨10.1016/j.jmva.2018.04.009⟩. ⟨hal-01553839v3⟩