We take another look at using Stein's method to establish uniform Berry-Esseen bounds for Studentized nonlinear statistics, highlighting variable censoring and an exponential randomized concentration inequality for a sum of censored variables as the essential tools to carry the arguments involved. As an important application, we prove a uniform Berry-Esseen bound for Studentized U-statistics in a form that exhibits the dependence on the degree of the kernel.

翻译：本文重新审视了利用Stein方法建立Student化非线性统计量的一致Berry-Esseen界的问题，强调变量截断技术以及截断变量和指数型随机化集中不等式在推进相关论证中的核心作用。作为重要应用，我们证明了Student化U统计量的一致Berry-Esseen界，其表达形式明确展示了界对核函数阶数的依赖关系。