Total variation bounds in the Lindeberg central limit theorem

TL;DR

This paper establishes explicit bounds on the total variation distance in the Lindeberg CLT, demonstrating that Lindeberg's condition is both necessary and sufficient for convergence in this metric.

Contribution

It provides the first explicit total variation bounds for the Lindeberg CLT, clarifying the exact conditions for convergence.

Findings

Lindeberg's condition is necessary and sufficient for total variation convergence.

Explicit bounds quantify the rate of convergence in total variation.

Results apply to sums of non-i.i.d. random variables.

Abstract

In this paper, we obtain an explicit total variation bound in the central limit theorem for the sums of non-i.i.d. random variables. Our results show that, under suitable assumptions, Lindeberg's condition is sufficient and necessary for the convergence in total variation distance.