Some improved results on Berry–Esséen bounds for strong mixing random variables and applications

In this paper, we mainly establish a general form of Berry–Esséen bound for α-mixing random variables. With different choices of the parameters, the rates are shown as O(n−3/26), O(n−1/6), and approximately O(n−1/4). These results improved some corresponding ones in the literature. An application to the Berry–Esséen bound of sample quantiles is further provided. Moreover, some simulations are also carried out to support the theoretical results.