Bounds of the remainder in a combinatorial central limit theorem

TL;DR

This paper establishes new bounds for the remainder in a combinatorial central limit theorem, applicable without independence or moment assumptions, extending classical inequalities and including cases with infinite variations.

Contribution

It introduces bounds that do not require independence or finite moments, broadening the applicability of the combinatorial CLT and deriving new inequalities.

Findings

New bounds for the remainder in combinatorial CLT

Extensions of Esseen and Berry-Esseen inequalities

Applicability to infinite variation cases

Abstract

We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type inequalities, some other new bounds and a combinatorial central limit theorem in the case of infinite variations.