U-max-Statistics
Statistics Theory
2007-05-23 v1 Probability
Statistics Theory
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.
Cite
@article{arxiv.0704.1379,
title = {U-max-Statistics},
author = {Wei Lao and Michael Mayer},
journal= {arXiv preprint arXiv:0704.1379},
year = {2007}
}
Comments
16 pages