On asymptotic behavior of U-statistics for associated random variables

Let ${X_n, n \ge 1}$ be a sequence of stationary associated random variables. For such a sequence, we discuss the limiting behavior of U-statistics based on kernels which are of bounded Hardy-Krause variation. As an application, we obtain the asymptotic distribution of Gini's mean difference. We also give simulation results to illustrate the asymptotic normality of the statistic under the dependent setup.