On the estimation of the mean of a random vector

TL;DR

This paper proves the existence of a non-asymptotic sub-Gaussian estimator for the mean of a multivariate distribution, applicable under mild moment conditions, advancing statistical estimation methods.

Contribution

It introduces a new estimator with guaranteed sub-Gaussian performance for all distributions meeting mild moment assumptions.

Findings

Existence of a sub-Gaussian estimator for multivariate means.

The estimator works under mild moment conditions.

Performance guarantees are non-asymptotic.

Abstract

We study the problem of estimating the mean of a multivariatedistribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.