In this paper, the Bahadur representation of sample quantiles for φ-mixing random variables is investigated without any restriction on the decaying rate of mixing coefficients. As an application, we further investigate the asymptotic normality and the Berry–Esséen bound of sample quantiles for φ-mixing random variables under some general conditions. It is shown that the rate of normal approximation is $O\left(n^{-1/6+\kappa }\right)$ for any $0<\kappa <1/6$ if the mixing coefficients satisfy $\phi \left(n\right)=O\left(n^{-\text{β}}\right)$ for some $\text{β}\ge 3/2$ or $O\left(n^{-1/4+\rho }\right)$ for any $0<\rho <1/4$ if the mixing coefficients can decay exponentially. Furthermore, a real data analysis is presented.

在本文中，研究了φ混合随机变量的样本分位数的 Bahadur 表示，对混合系数的衰减率没有任何限制。作为应用，我们进一步研究了一些一般条件下φ混合随机变量的渐近正态性和样本分位数的 Berry-Esséen 界。结果表明，正态逼近率为$哦\left(n^{-1/6+\kappa }\right)$ 对于任何 $0<\kappa <1/6$ 如果混合系数满足 $\phi \left(n\right)=哦\left(n^{-\text{β}}\right)$ 对于一些 $\text{β}\ge 3/2$ 或者 $哦\left(n^{-1/4+\rho }\right)$ 对于任何 $0<\rho <1/4$如果混合系数可以指数衰减。此外，还提供了真实的数据分析。