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arXiv · 2301.02098

Another look at Stein's method for Studentized nonlinear statistics with an application to U-statistics

Dennis Leung·Qi-Man Shao·Liqian Zhang
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Abstract

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.

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Dennis Leung, Qi-Man Shao, Liqian Zhang. 2023-01-05. Another look at Stein's method for Studentized nonlinear statistics with an application to U-statistics. https://arxiv.org/abs/2301.02098

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