Explicit error bounds for lattice Edgeworth expansions

TL;DR

This paper develops explicit error bounds for the Edgeworth expansion of sums of bounded lattice random variables, aiding in precise probabilistic approximations.

Contribution

It provides the first explicit and effective bounds on the errors in the one-term Edgeworth expansion for lattice sums.

Findings

Derived explicit error bounds for lattice Edgeworth expansions

Improved accuracy in probabilistic approximations of lattice sums

Applicable to comparing mean and median of IID sums

Abstract

Motivated, roughly, by comparing the mean and median of an IID sum of bounded lattice random variables, we develop explicit and effective bounds on the errors involved in the one-term Edgeworth expansion for such sums.