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 language | English |
|---|---|
| Pages (from-to) | 3089-3151 |
| Number of pages | 63 |
| Journal | Journal of Theoretical Probability |
| Volume | 37 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Nov 2024 |
| Externally published | Yes |
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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