On asymptotic normality form-dependentU-statistics

[摘要] Let(Xn)be a sequence ofm-dependent random variables, not necessarily equally distributed. We give a Berry-Esseen estimate of the convergence to normality of a suitable normalization of aU-statistic of the(Xn). This bound holds under moment assumptions quite weaker than the existence of third moments for the kernel. Since we obtain the sharpest bound, the order of the bound can not be improved.

[学科分类] 数学（综合）