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arXiv · 0704.1379

U-max-Statistics

Wei Lao·Michael Mayer
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Abstract

In 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.

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Wei Lao, Michael Mayer. 2007-04-11. U-max-Statistics. https://arxiv.org/abs/0704.1379

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