Central Limit Theorems and Approximation Theory: Part II

2023/06/26 by Kuchibhotla, Arun Kumar
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2306.14382

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.

Related

• Central Limit Theorems and Approximation Theory: Part I
• A comparison theorem under sublinear expectations and related limit theorems
• A radial version of the Central Limit Theorem
• A Uniform-in-P Edgeworth Expansion under Weak Cramér Conditions
• Two multivariate central limit theorems