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A weighted U-statistic based on a random sample X1,…,Xn has the form Un=∑1≤i,j≤nwi−jK(Xi,Xj), where K is a fixed symmetric measurable function and the wi are symmetric weights. A large class of statistics can be expressed as weighted U-statistics or variations thereof. This paper establishes the asymptotic normality of Un when the sample observations come from a nonlinear time series and linear processes.
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