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 $O(n^{-1/2}{\hspace{0.17em}\text{log}\hspace{0.17em}}^{2}n)$ if the covariances decrease exponentially to 0. The best rate is shown as $O(n^{-1/3})$ under a polynomial decay of the covariances.

中文翻译：

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关联样本分位数的 Berry-Esseen 定理

摘要

本文研究了相关随机变量样本分位数在一定条件下协方差衰减的一致渐近正态性。我们获得了正态近似阶数$○(n^{-1/2}{\hspace{0.17em}\text{日志}\hspace{0.17em}}^{2}n)$如果协方差呈指数下降到 0。最佳比率显示为$○(n^{-1/3})$在协方差的多项式衰减下。