Non-uniform bounds in normal approximation for matrix correlation statistics and idependent bounded random variables

Abstract

This thesis contains two main parts. In the first part, let (a[subscript ij]) and (b[subscript ij]) be n x n matrices of real numbers and pi a random permutation of {1, 2, ...,n}. Under a boundedness condition, we establish non-uniform bounds in normal approximation for V and W by using a concentration inequality approach of Stein's method. In the second part, let X1, X2, ..., Xn be independent bounded random variables. We give a non-uniform bound in normal approximation for X1 + X2 +...+Xn by using Stein's method without using the concentration inequality approach.