Abstract
Assuming the existence of fourth moment only, we prove the Berry-Esseen theorem for $U$-statistics. Assuming the third absolute moment, we obtain the order bound $O(n^{-\frac{1}{2}} \log^{\frac{1}{3}}n)$. This improves earlier results of Bickel, and Grams and Serfling.
Citation
Y.-K. Chan. John Wierman. "On the Berry-Esseen Theorem for $U$-Statistics." Ann. Probab. 5 (1) 136 - 139, February, 1977. https://doi.org/10.1214/aop/1176995897
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