We define the local empirical process, based on n i.i.d. random vectors in dimension d, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that for these local empirical processes, indexed by classes of sets that vary with n and...

Let (X1, Y1), … , (Xn, Yn) be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima max( Xi) and max(Yi) is then characterized by the...