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In this paper we obtain the distance between U-statistics and a normal random variable by utilizing Zolotarev’s ideal metric. The results are for U-statistics based on i.i.d random variables as well as for U-statistics based on negatively associated random variables. Corresponding results are also investigated for the related class of von Mises statistics.

Asymptotic normality of U-statistics based on i.i.d. or negatively associated observations by utilizing Zolotarev’s ideal metric