# Gaussian Approximations for Maxima of Random Vectors under $(2+\iota)$-th Moments

## TL;DR

This paper establishes a nonasymptotic Gaussian approximation for the maximum of sums of random vectors with $(2+ ext{iota})$-th moments, providing a versatile tool for statistical learning applications.

## Contribution

It introduces a novel nonasymptotic Gaussian approximation theorem applicable to sums of random vectors with limited moments, using new technical methods.

## Key findings

- Provides a general Gaussian approximation result for maxima of random vectors
- Applicable to various statistical learning problems
- Employs innovative proof techniques including Lindeberg telescoping

## Abstract

We derive a Gaussian approximation result for the maximum of a sum of random vectors under $(2+\iota)$-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof uses the Lindeberg telescopic sum device along with some other newly developed technical results.