Stratified Permutational Berry--Esseen Bounds and Their Applications to Statistics

Fuente: arXiv
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Main Authors: Tian, Pengfei, Yang, Fan, Ding, Peng
Format: Preprint
Published: 2025
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author Tian, Pengfei
Yang, Fan
Ding, Peng
author_facet Tian, Pengfei
Yang, Fan
Ding, Peng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_13986
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stratified Permutational Berry--Esseen Bounds and Their Applications to Statistics
Tian, Pengfei
Yang, Fan
Ding, Peng
Statistics Theory
62E17, 60F05 (Primary) 62K10 (Secondary)
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.
title Stratified Permutational Berry--Esseen Bounds and Their Applications to Statistics
topic Statistics Theory
62E17, 60F05 (Primary) 62K10 (Secondary)
url https://arxiv.org/abs/2503.13986