The Bahadur representation for sample quantiles under weak dependence

In this paper, we give a Bahadur representation of sample quantiles based on strongly mixing random variables under polynomially decaying rate. Our results extend Theorems 1 and 2 of Yoshihara [1995. The Bahadur representation of sample quantile for sequences of strongly mixing random variables. Statist. Probab. Lett. 24, 299–304].