Sub-Gaussian mean estimators

TL;DR

This paper explores the design and limitations of mean estimators that exhibit sub-Gaussian performance for heavy-tailed distributions, providing both constructive methods and impossibility results.

Contribution

It introduces estimators with sub-Gaussian properties for heavy-tailed data and establishes fundamental limitations on mean estimation.

Findings

Proposes estimators with sub-Gaussian tails for heavy-tailed distributions

Proves impossibility results for certain mean estimators

Analyzes non-asymptotic estimation bounds

Abstract

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a sub-Gaussian behavior even for certain heavy-tailed distributions. We also prove various impossibility results for mean estimators.