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Berry-Esseen Theorem for Sample Quantiles with Locally Dependent Data

Year: 2025

Type: article

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.

Source: Latin American Journal of Probability and Mathematical Statistics

DOI: 10.30757/alea.v22-20

Authors: Partha S. Dey, Grigory Terlov

Institutions: University of Illinois Urbana-Champaign, University of North Carolina at Chapel Hill

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4408813263

FWCI:

Cites: 25

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Related to: 10