International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 187-199

On asymptotic normality for m-dependent U-statistics

Wansoo T. Rhee

Faculty of Management Sciences, The Ohio State University, Columbus 43210, Ohio, USA

Received 21 April 1986

Copyright © 1988 Wansoo T. Rhee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.