Another Look at Stein’s Method for Studentized Nonlinear Statistics with an Application to U-Statistics

Dennis Leung (), Qi-Man Shao () and Liqian Zhang ()
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Dennis Leung: University of Melbourne
Qi-Man Shao: Southern University of Science and Technology
Liqian Zhang: University of Melbourne

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3089-3151

Abstract: 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 out 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.

Keywords: Stein’s method; Studentized nonlinear statistics; Variable censoring; Randomized concentration inequality; U-statistics; Self-normalized limit theory; Uniform Berry–Esseen bound; 62E17 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01350-4

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