U-max-statistics

Authors:
W. Lao;M. Mayer
Affiliations:
Institute of Stochastics, University of Karlsruhe, Englerstrasse 2, Karlsruhe, 76128, Germany;Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
Venue:
Journal of Multivariate Analysis
Year:
2008

Citing 1
Cited 1

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Fast surrogates of U-statistics

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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.