Berry-Esseen Bounds Via Exchangeable Pairs And Their Applications

The central limit theorem gives the weak convergence for the sum of random variables to the standard normal distribution, while the Berry-Esseen inequality provides an error bound of the approximation. Along with the development of Stein’s method, it is of great convenience to obtain Berry-Esseen bounds.In this thesis, by applying a newly developed Berry-Esseen bound via exchangeable pairs, we obtain the Berry-Essen bound for an independence test statistic. The independence test statistic based on the sum of squared sample correlation coefficients was introduced by Schott(2005) Testing for complete independence in high dimensions, and its asymptotic normality was also proved. In this thesis, an optimal Berry-Esseen bound of O(m-1/2) is obtained when the population has a finite of twelfth moment.