We establish nonuniform Berry-Esseen (B-E) bounds for Studentized U-statistics of the rate $1/\sqrt{n}$ under a third-moment assumption, which covers the t-statistic that corresponds to a kernel of degree 1 as a special case. While an interesting data example raised by Novak (2005) can show that the form of the nonuniform bound for standardized U-statistics is actually invalid for their Studentized counterparts, our main results suggest that the validity of such a bound can be restored by minimally augmenting it with an additive term that decays exponentially in n. To our best knowledge, this is the first time that valid nonuniform B-E bounds for Studentized U-statistics have appeared in the literature.

翻译：我们建立了在第三矩假设下，学生化U统计量具有速率$1/\sqrt{n}$的非均匀Berry-Esseen（B-E）界，该结果涵盖了作为特例的t统计量（对应阶数为1的核）。尽管Novak（2005）提出的有趣数据实例表明，标准化U统计量的非均匀界形式实际上对其学生化对应形式无效，但我们的主要结果表明，通过最小程度地添加一个随n指数衰减的加性项，可以恢复该界的有效性。据我们所知，这是文献中首次出现学生化U统计量的有效非均匀B-E界。