Sub-Gaussian mean estimators
Luc Devroye, Matthieu Lerasle, Gabor Lugosi, Roberto I. Oliveira
The Annals of Statistics · 2016 · Volume 44 · Issue 6
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 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.
Keywords
60F99, 62G05, minimax bounds, Sub-Gaussian estimators
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