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

Dennis Leung*, Qi Man Shao, Liqian Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal Articlepeer-review

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.

Original languageEnglish
Pages (from-to)3089-3151
Number of pages63
JournalJournal of Theoretical Probability
Volume37
Issue number4
DOIs
Publication statusPublished - Nov 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

  • 62E17
  • Randomized concentration inequality
  • Self-normalized limit theory
  • Stein’s method
  • Studentized nonlinear statistics
  • U-statistics
  • Uniform Berry–Esseen bound
  • Variable censoring

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