分层置换 Berry--Esseen 引理及其统计学中的应用
摘要
the stratified linear permutation statistic arises in various statistics problems, including stratified and post-stratified survey sampling, stratified and post-stratified experiments, conditional permutation tests, etc. although we can derive the berry--esseen bounds for the stratified linear permutation statistic based on existing bounds for the non-stratified statistics, those bounds are not sharp, and moreover, this strategy does not work in general settings with heterogeneous strata with varying sizes. we first use stein's method to obtain a unified stratified permutational berry--esseen bound that can accommodate heterogeneous strata. we then apply the bound to various statistics problems, leading to stronger theoretical quantifications and thereby facilitating statistical inference in those problems.
引用
@article{arxiv.2503.13986,
title = {Stratified Permutational Berry--Esseen Bounds and Their Applications to Statistics},
author = {Pengfei Tian and Fan Yang and Peng Ding},
journal= {arXiv preprint arXiv:2503.13986},
year = {2026}
}