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Berry-Esseen Theorem for Sample Quantiles with Locally Dependent Data

Probability 2025-03-05 v2 Statistics Theory Statistics Theory

Abstract

We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying Stein's method for local dependence, and bounding the distance between two normal distributions. We also generalize this approach to the joint convergence of sample quantiles with an explicit convergence rate.

Keywords

Cite

@article{arxiv.2208.09072,
  title  = {Berry-Esseen Theorem for Sample Quantiles with Locally Dependent Data},
  author = {Partha S. Dey and Grigory Terlov},
  journal= {arXiv preprint arXiv:2208.09072},
  year   = {2025}
}

Comments

19 pages, a revised version, to appear in ALEA

R2 v1 2026-06-25T01:48:34.023Z