Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 350517, 8 pages
Research Article

Asymptotics for the Moment Convergence of U-Statistics in LIL

School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received 18 September 2009; Accepted 18 January 2010

Academic Editor: Andrei Volodin

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.


Let Un be a U-statistic based on a symmetric kernel h(x,y) and i.i.d. samples {X,Xn;n1}. 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.