U-max-statistics

W. Lao and M. Mayer

Journal of Multivariate Analysis, 2008, vol. 99, issue 9, 2039-2052

Abstract: In 1948, W. Hoeffding [W. Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Statist. 19 (1948) 293-325] 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 a 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.

Keywords: 60D05; 60F05; 60G70; Random; diameter; Triameter; Spherical; distance; Extreme; value; U-statistics; Poisson; approximation (search for similar items in EconPapers)
Date: 2008
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