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 dependence models. On the contrary, in many applications data do not comply with asymptotic dependence models and in such cases there are less guidelines available. This is especially true when considering the componentwise maxima approach. In this paper we contribute to extending this part. 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. We propose an estimator of the latter and we study its main asymptotic properties and its performance is illustrated by a simulation study.

Domaines: Statistiques [math.ST]

Armelle Guillou, Simone A. Padoan, Stefano Rizzelli. INFERENCE FOR ASYMPTOTICALLY INDEPENDENT SAMPLES OF EXTREMES. 2017. ⟨hal-01553839v1⟩