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

Pengfei Tian; Fan Yang; Peng Ding

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arXiv · 2503.13986

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

Pengfei Tian·Fan Yang·Peng Ding

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Abstract

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.

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Pengfei Tian, Fan Yang, Peng Ding. 2025-03-18. Stratified Permutational Berry--Esseen Bounds and Their Applications to Statistics. https://arxiv.org/abs/2503.13986

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