A Berry-Esseen theorem for sample quantiles under association. Issue 18 (17th September 2022)

• Record Type: Journal Article
• Authors: Douge, Lahcen
• Is Part Of: Communications in statistics. Volume 51:Issue 18(2022)
• Page Start: 6515
• Page End: 6528
• Publication Date: 2022-09-17
• Subjects: Berry-Esseen bound -- sample quantiles -- associated random variables; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2020.1862871
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this paper, the uniformly asymptotic normality for sample quantiles of associated random variables is investigated under some conditions on the decay of the covariances. We obtain the rate of normal approximation of order O ( n − 1 / 2 log 2 n ) if the covariances decrease exponentially to 0. The best rate is shown as O ( n − 1 / 3 ) under a polynomial decay of the covariances.