On minimal moment assumptions in Berry-Esseen theorems for U-statistics

Bentkus V, Götze F. On minimal moment assumptions in Berry-Esseen theorems for U-statistics. THEORY OF PROBABILITY AND ITS APPLICATIONS. 1996;40(3):430-445.The rate of convergence for asymptotically normal U-statistics is of order O(n(-1/2)) provided that E\E{h(X(1), X(2))/X(1)}\(3) 0. In this paper we extend the result for statistics of higher orders and with possible nonnormal limit distributions