2009/06/06 by Michael Mayer, Mayer, Michael
Environmental Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Soil Geostatistics and Mapping #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.0906.1266
openalex publication_date 2009/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.