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- W2000653469 abstract "Recent results on the Berry-Esseen bound for $U$-statistics assumed the following conditions: Suppose a $U$-statistic (of degree 2) is nondegenerate. Then the rate of convergence in the CLT is of the order $O(n^{-1/2})$ provided that $mathbb{E}|mathbb{E}{h(X_1, X_2)|X_1}|^3 < infty, mathbb{E}|h(X_1, X_2)|^{5/3} < infty,$ where $h$ is a symmetric kernel corresponding to the $U$-statistic. It follows from our results that these moment conditions are final. In particular, the last moment condition cannot be replaced by a moment of order $5/3 - epsilon$ for any $epsilon > 0$. Similar results hold for von Mises statistics." @default.
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- W2000653469 date "1994-10-01" @default.
- W2000653469 modified "2023-09-28" @default.
- W2000653469 title "Lower Estimates of the Convergence Rate for $U$-Statistics" @default.
- W2000653469 doi "https://doi.org/10.1214/aop/1176988478" @default.
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