Diagnostics for pairwise region extremal dependence in random fields

The coefficient of tail dependence η and a slowly varying function L provide information about pairwise extremal dependence of a max-stable spatial process. They enable to know whether the spatial process is asymptotically dependent, asymptotically independent or independent for any pair of locations i and j. We propose a generalization of such diagnostic tools in order to quantify the dependence for any pair of sets A and B of locations. We illustrate the properties and use of such measures through theoretical examples