An improvement of Tusn\'ady's inequality in the bulk

TL;DR

This paper presents a non-asymptotic generalization of a refined continuity correction for the Binomial distribution, leading to improved versions of Tusnady's inequality in the bulk, enhancing approximation accuracy.

Contribution

It introduces a non-asymptotic generalization of a continuity correction and improves Tusnady's inequality for the Binomial distribution in the bulk region.

Findings

Enhanced bounds for Tusnady's inequality in the bulk

Non-asymptotic generalization of a Binomial continuity correction

Improved approximation accuracy in probabilistic bounds

Abstract

We prove a non-asymptotic generalization of the refined continuity correction developed in Cressie (1978) for the Binomial distribution, which we then use to improve the versions of Tusn\'ady's inequality from Massart (2002) and Carter & Pollard (2004) in the bulk.