The Study Of Berry--Esseen Bound For Negatively Associated Sequence And Its Application

In this paper, we investigate some limit theories for NA sequence of ran-dom variables. First of all, we investigate the Berry-Esseen bound for the sequence of negatively associated (NA) random variables. Under some dif-fident conditions, the Berry-Esseen bounds are presented as O(n-1//4log n log log n)、O(n-1/6logn·log log n) and O(n-1/6log n). Secondly, Based on the convergence rate O(n-1/6log n), we investigate the Berry-Esseen bound of sample quantiles for NA random variables and obtain the rate O(n-1/6log n) by using moment inequality for NA random variables, Berry-Esseen inequali-ty, block ideas and other tools. Our results extend the corresponding ones in the literature.It is well known that Berry-Esseen theorem, which is used to study the convergence rate of the central limit theorem, and it can been found in many monographs such as Shiryaev,Petrov, Cai and Roussas, Yang et al.ect..The central limit theorem is the most important in probability theory, and it shows the sums of distribution for the random variable sequence asymptotically normal distribution. The central limit theorem, which is the basis of statistical and error analysis, and possess a wide range of practical applications. From1919to1925, theory of characteristic function systemat-ically established by Levy, the research about the central limit theorem has been developed rapidly. From then on, a general limit theorem and local limit theorem are been emerged. Limit theorem plays important role in probability theory. Furthermore, it is the cornerstones of mathematical statistics. Proba-bility theory analysis which is formed in the course of research limit theorem has impact on the development of probability theory for a long time. There-fore, the studies of NA random variables and its applications are meaningful. Moreover, our results extend the corresponding ones in the literature.