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.