International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 187-200
doi:10.1155/S0161171288000225

On asymptotic normality for m-dependent U-statistics

Abstract

Let (Xn) be a sequence of m-dependent random variables, not necessarily equally distributed. We give a Berry-Esseen estimate of the convergence to normality of a suitable normalization of a U-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.