Asymptotics for the Moment Convergence of <inline-formula> <graphic file="1029-242X-2010-350517-i1.gif"/></inline-formula>-Statistics in LIL

Abstract

Let be a -statistic based on a symmetric kernel and i.i.d. samples . In this paper, the exact moment convergence rates in the law of the iterated logarithm and the law of the logarithm of are obtained, which extend previous results concerning partial sums.