Bounds are provided for the rates of convergence in the central limit theorem and the strong law of large numbers for U-statistics. The results are obtained by establishing suitable bounds upon the moments of the difference between a U-statistic and its projection. Analogous conclusions for the associated von Mises statistical functions are indicated. Statistics considered for exemplification are the sample variance and the Wilcoxon two-sample statistic.
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Grams et al. (1973) studied this question.
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