The Bahadur representations of quantile estimators in general unequal probability sampling

In this study, we establish the Bahadur representations of quantile estimators based on the Hájek and the Horvitz–Thompson estimators for the population distribution function in unequal probability sampling designs under general conditions. We also present the asymptotic normality of the above quantile estimators. The simulation studies using real data confirm the validity of the asymptotic normality.