The Bahadur representation of sample quantiles for φ-mixing random variables and its application

Abstract

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 for any if the mixing coefficients satisfy for some or for any if the mixing coefficients can decay exponentially. Furthermore, a real data analysis is presented.