Inference for asymptotically independent samples of extremes

An important topic in 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 component-wise 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.