Let be a sequence of stationary associated random variables. Based on this sample, we establish a central limit theorem for U-statistics with monotonic kernels of degree 3 and above using the Hoeffding's decomposition. We also extend these results to U-statistics based on non-monotonic functions. We also obtain a consistent estimator of , where , , and is a non-monotonic function, using the ideas of Peligrad and Suresh .
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