Sub-Gaussian mean estimators

Authors: Luc P Devroye, Matthieu Lerasle and Gábor Lugosi

Annals of Statistics, Vol. 44, No 6, 2695-2725, December, 2016

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a nonasymptotic 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.