Bounds of the remainder in a combinatorial central limit theorem

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.

References in corpus (2)

• Berry Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing
• Esseen type bounds of the remainder in a combinatorial CLT