Limit properties for multivariate extreme values in sequences of independent, non-identically distributed random vectors
Let \(M_ n\) be the vector of componentwise maxima of independent random vectors \(X_ i\), \(1\leq i\leq n\). Let \(a_ n>0\) and \(b_ n\) be such that \((M_ n-b_ n)/a_ n\) converges in distribution to a nondegenerate random vector with df G. In general G can be any df; but not so when each \(X_ i\) is uniformly asymptotic negligible with respect to the norming constants. Under one such condition, the structure of G is characterized, generalizing the univariate discussion in \textit{J. Galambos}, The asymptotic theory of extreme order statistics. 2nd ed. (1987; Zbl 0634.62044), p. 217. Furthermore, the dependence structure of G is analyzed. Conditions are given which ensure that G (i) has independent components, (ii) is max- infinite divisible, (iii) is associated, and (iv) is an extreme value df.
componentwise maxima of independent random vectors
scientific article; zbMATH DE number 4107923
scientific article