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.
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