Berry-Esseen Theorem for Sample Quantiles with Locally Dependent Data

TL;DR

This paper establishes a Gaussian CLT for sample quantiles derived from locally dependent data, providing explicit convergence rates and a generalized approach for joint quantile convergence.

Contribution

It introduces a novel method using Stein's technique to analyze the distribution of sample quantiles under local dependence, with explicit convergence bounds.

Findings

Gaussian CLT for sample quantiles with local dependence

Explicit convergence rates provided

Generalization to joint quantile convergence

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.