Berry-esseen bounds for random statistics via Stein's method

Abstract

The purpose of this dissertation is to obtain Berry-Esseen bounds for random summation via Stein’s method.Especially, we focus on random-index statistics and the linearity of them. We improve the bounds for random sums of independent random variables which are examples of random-index linear statistics. We also provide the bounds for random-index non-linear statistics. As an example of random-index non-linear statistics, we obtain the bounds for random U-statistics. Moreover, we extend the results to multi-sample random U-statistics and derive the bounds for random-sum Wilcoxon statistics as an application of two-sample random U-statistics.