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<p/> <p>Let <inline-formula> <graphic file="1029-242X-2010-350517-i2.gif"/></inline-formula> be a <inline-formula> <graphic file="1029-242X-2010-350517-i3.gif"/></inline-formula>-statistic based on a symmetric kernel <inline-formula> <graphic file="1029-242X-2010-350517-i4.gif"/></inline-formula> and i.i.d. samples <inline-formula> <graphic file="1029-242X-2010-350517-i5.gif"/></inline-formula>. In this paper, the exact moment convergence rates in the law of the iterated logarithm and the law of the logarithm of <inline-formula> <graphic file="1029-242X-2010-350517-i6.gif"/></inline-formula> are obtained, which extend previous results concerning partial sums.</p>