Gaussian approximation of moments of sums of independent random variables

TL;DR

This paper advances the understanding of the moments of sums of independent random variables, especially for the case when the moment order is between 2 and 4, using a combinatorial approach for even moments.

Contribution

It generalizes previous results on $p$-th moments for $2 \,\leq p \,\leq 4$ and introduces a new combinatorial method for analyzing even moments.

Findings

Improved estimates for $p$-th moments when $2 \,\leq p \,\leq 4$

Development of a combinatorial approach for even moments

Extension of Lata{}'s results on moment estimates

Abstract

We continue the research of Lata{\l}a on improving estimates of $p$-th moments of sums of independent random variables. We generalize some of his results in the case when $2 \leq p \leq 4$ and present a combinatorial approach for even moments.