Non-asymptotic tails estimations for sums of random vectors having moderate decreasing tails

TL;DR

This paper provides precise non-asymptotic tail estimates for sums of independent random vectors with moderate decreasing tails, enhancing understanding of their distributional behavior in finite samples.

Contribution

It introduces sharp uniform tail estimations for sums of independent vectors with moderate decreasing tails, filling a gap in non-asymptotic tail analysis.

Findings

Derived sharp non-asymptotic tail bounds for sums of vectors.

Applicable to vectors with moderate decreasing tail behavior.

Improves finite-sample tail probability estimates.

Abstract

We derive the sharp non-asymptotical uniform estimations for tails of distributions for classical normed sums of centered normed independent random vectors having a moderate decreasing individual tails of summands.