Esseen type bounds of the remainder in a combinatorial CLT

TL;DR

This paper establishes bounds similar to Esseen's for the error term in a combinatorial central limit theorem involving independent variables that lack third moments, advancing the understanding of convergence rates.

Contribution

It introduces Esseen type bounds for the remainder in a combinatorial CLT without requiring third moments, extending previous results to broader conditions.

Findings

Derived explicit bounds for the remainder term

Extended CLT error analysis to variables without third moments

Provided theoretical tools for combinatorial probability approximations

Abstract

We derive Esseen type bounds of the remainder in a combinatorial central limit theorem for independent random variables without third moments.