A Berry-Esseen theorem for sample quantiles under association

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.