Abstract
Let {Zn, n≥1} be a sequence of nonnegative, weakly dependent random variables, and , where is an array of nonnegative weights. We show that can be asymptotically approximated by for a class of functions f(·) satisfying some mild conditions. Under some general conditions, we also prove that the expectation approximates to with a certain convergence rate for any a > 0 and , where . The results obtained in the article improve and extend some corresponding ones in the literature. Some numerical simulations and a real data example are also provided to support the theoretical results.
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