Some Properties of U Statistics

U statistics possess many desirable properties, such as unbiasedness and asymptotic normality (under mild conditions); however, there do not appear to be widely known results whereby one can determine whether a given statistic is a U statistic.This article gives such results, in addition to a method for finding the kernel.Also, a relationship between the jackknife procedure and these properties is shown, resulting in an interesting characterization of U statistics.