On Estimating the Asymptotic Variance of a Function of U Statistics

The asymptotic variance of a function of several U statistics was given by Hoeffding (1948).Another approach, shown to give identical results, is the infinitesimal jackknife technique (Jaeckel 1972).In this article I illustrate the different types of calculations involved in the two methods via two examples.I show that although the infinitesimal jackknife is not often used in practice, the tools can be used to help obtain the variance of a function of several U statistics.This approach illustrates another application of influence functions.