Journal of Inequalities and Applications (Jan 2010)
Asymptotics for the Moment Convergence of U-Statistics in LIL
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.