Central Limit Theorems and Approximation Theory: Part II

TL;DR

This paper extends previous work on bounding expectation differences between sums of independent vectors and Gaussian limits by employing Edgeworth expansions and integral representations, enhancing approximation techniques.

Contribution

It introduces new bounds using Edgeworth expansions and integral representations, advancing the approximation theory for sums of independent random vectors.

Findings

Derived finite sample bounds for expectation differences

Established integral representation theorems for approximation

Enhanced understanding of Gaussian approximation accuracy

Abstract

In Part I of this article (Banerjee and Kuchibhotla (2023)), we have introduced a new method to bound the difference in expectations of an average of independent random vector and the limiting Gaussian random vector using level sets. In the current article, we further explore this idea using finite sample Edgeworth expansions and also established integral representation theorems.