Asymptotic development for the CLT in total variation distance

TL;DR

This paper develops an asymptotic expansion in total variation distance for the CLT, providing explicit formulas for the approximation error when the underlying distribution has an absolutely continuous component.

Contribution

It introduces a detailed asymptotic expansion in total variation for the CLT under specific regularity conditions, with explicit formulas for the approximation measure.

Findings

Explicit error expansion in powers of n^{-1/2}

Formula for the approximating measure in total variation

Conditions for the law to be locally lower-bounded by Lebesgue measure

Abstract

The aim of this paper is to study the asymptotic expansion in total variation in the Central Limit Theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely continuous component): we develop the error in powers of $n^{-1/2}$ and give an explicit formula for the approximating measure.