A Berry-Esseen bound for U-statistics in the non-IID case

Let X-1 ,..., X-n be independent, not necessarily identically distributed random variables. An optimal Berry Esseen bound is derived for U-statistics of order 2, that is, statistics of the form T = Sigma(1 less than or equal to i<j less than or equal to n) g(ij) (X-i, X-j), where the g(ij) are measurable functions such that if E \g(j)(X-i, X-j)\ < infinity. An application is given concerning Wilcoxon's rank-sum test.