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

01/05/2023

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by   Dennis Leung, et al.

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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 with a kernel of any given degree.