Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem

TL;DR

This paper develops an Edgeworth-type expansion for the entropy distance to normality in the entropic CLT, under minimal moment assumptions, providing refined asymptotic approximations.

Contribution

It introduces a new Edgeworth expansion for entropy distance in the entropic CLT with minimal moment conditions, advancing theoretical understanding.

Findings

Established an Edgeworth-type expansion for entropy distance

Applicable to sums of i.i.d. variables with minimal moments

Provides refined asymptotic approximations in the entropic CLT

Abstract

An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.