A Berry–Esseen theorem for sample quantiles under martingale difference sequences.

In this paper, we establish the uniformly asymptotic normality for sample quantiles based on martingale difference sequences under some suitable conditions. We obtain the rate of normality approximation of O (n − 1 / 4 log ⁡ n) by using some classical methods such as Bernstein type inequality, and so on. Finally, we verify asymptotic normality for the fixed quantile of the martingale difference sequences and present some numerical simulations to demonstrate the finite sample performances of the theoretical results. [ABSTRACT FROM AUTHOR]