Some improved results on Berry-Esseen bounds for strong mixing random variables and applications

In this paper, we mainly establish a general form of Berry-Esseen bound for a-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-Esseen bound of sample quantiles is further provided. Moreover, some simulations are also carried out to support the theoretical results.