APPROXIMATION RATES FOR MULTIVARIATE EXCEEDANCES

This article deals with the Poisson approximation of processes of pathwise or componentwise defined exceedances; the approximations are carried out in terms of the variational distance. Bounds on the accuracy of these approximations are given by means of survivor functions. Moreover, the concept of a delta-neighborhood of a generalized Pareto d.f. will be extended from the univariate setting to the bivariate one. Finally, approximate distributions of bivariate extreme and intermediate order statistics are deduced from the point process result.