Convergence rates for u-statistics and related statistics

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.