Copyright © 2010 Ke-Ang Fu. 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.

Abstract

Let Un be a U-statistic based on a symmetric kernel h(x,y) and i.i.d. samples {X,Xn;n≥1}. In this paper, the exact moment convergence rates in the law of the iterated logarithm and the law of the logarithm of Un are obtained, which extend previous results concerning partial sums.