The rate of convergence to the normal law in terms of pseudomoments

TL;DR

This paper investigates how quickly sums of i.i.d. random variables approach a normal distribution, using pseudomoments to quantify the convergence rate, extending previous methods to higher orders.

Contribution

It introduces a novel approach utilizing truncated pseudomoments to estimate the convergence rate of sums of i.i.d. variables to the Gaussian law, surpassing the classical $n^{-1/2}$ rate.

Findings

Established convergence rates in terms of pseudomoments

Extended estimates to higher orders beyond $n^{-1/2}$

Applied Yu. Studnyev's idea for improved bounds

Abstract

We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting estimates of the rate of convergence of the order higher than $n^{-1/2}$.