Abstract
ABSTRACTIf a spatial process is isotropic then the usual pairwise extremal dependence measures depend only on the distance ‖i − j‖ between the locations i and j. Nevertheless, in general, we need to evaluate the spatial dependence in different directions of . In this paper, we consider matrices of multivariate tail and extremal coefficients where we table the degrees of dependence for chosen pairs of sets A and B of locations. In this multidirectional approach, the well-known relation between the bivariate tail dependence λ and the extremal ε coefficients, λ = 2 − ϵ, is generalized and new properties arise. The measure matrices here defined to describe spatial dependence are used in several random fields, including a new space time ARMAX storage model and an M4 random field.
Published Version
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