An improvement of a non-uniform bound for combinatorial central limit theorem

ABSTRACT

In this article, we develop a new Rosenthal Inequality for uniform random permutation sums of random variables with finite third moments and apply it to obtain a sharp non-uniform bound for the combinatorial central limit theorem using the Stein's method and the exchangeable pair techniques. The obtained bound is shown to be sharper than other existing bounds.

KEYWORDS:

• Combinatorial central limit theorem
• Exchangeable pair
• Stein's method
• Rosenthal inequality.

MATHEMATICS SUBJECT CLASSIFCATION:

• 60F05

Acknowledgements

The authors would like to thank the referees for all valuable comments that help this manuscript improved from the previous version. The first author would like to thank the Development and Promotion of Science and Technology Talents Project (DPST) and The 90th Anniversary of Chulalongkorn University Fund (Ratchadaphiseksomphot Endowment Fund) for financial support.