2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127197In 1948, W. Hoeffding introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued k-variate function h calculated at all possible sets of k points from a random sample. In the present paper we investigate the corresponding extreme value analogue, which we shall call U-max-statistics. We are concerned with the behavior of the largest value of such function h instead of its average. Examples of U-max-statistics are the diameter or the largest scalar product within a random sample. U-max-statistics of higher degrees are given by triameters and other metric invariants.16 pagesStatistics TheoryProbability62H11; 62E20text