Asymptotic normality for U-statistics of associated random variables

Let {Xn, n≥1} be a stationary sequence of associated random variables and Un be a U-statistic based on this sample. We establish a central limit theorem for Un when the U-statistic is degenerate or non-degenerate using an orthogonal expansion for the kernel associated with Un. We extend the results to U-statistics of kernels of degree 3 and to V-statistics of arbitrary degree. We also establish a central limit theorem for the two sample U-statistic based on observations of two independent stationary associated sequences