Dimension-free PAC-Bayesian bounds for the estimation of the mean of a random vector

TL;DR

This paper introduces a new mean estimator for random vectors that provides non-asymptotic, dimension-free, almost sub-Gaussian bounds under weak moment assumptions, using PAC-Bayesian inequalities.

Contribution

It proposes a novel mean estimator with dimension-free bounds, leveraging PAC-Bayesian techniques under weak moment conditions.

Findings

Non-asymptotic dimension-free bounds established

Estimator achieves almost sub-Gaussian tail behavior

Bounds hold under weak moment assumptions

Abstract

In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussian bounds are proved under weak moment assumptions, using PAC-Bayesian inequalities.