U-Quantile-Statistics

In 1948, W. Hoeffding introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present paper, we investigate the corresponding robust analogue which we call U-quantile-statistics. We are concerned with the asymptotic behavior of the sample p-quantile of such function h instead of its average. Alternatively, U-quantile-statistics can be viewed as quantile estimators for a certain class of dependent random variables. Examples are given by a slightly modified Hodges-Lehmann estimator of location and the median interpoint distance among random points in space.