U-statistic

Summary

A U-statistic is the average of a symmetric function, the kernel, over all subsets of a fixed size of the observations. It is an unbiased estimator of the mean of the kernel. The sample mean, the sample variance, Kendall's $\tau$ and the Mann–Whitney statistic are U-statistics or close relatives of them. Under mild conditions, Hoeffding's theory gives their asymptotic normality in one stroke.