Sub-Gaussian mean estimators

2015/09/19 by Devroye, Luc, Lerasle, Matthieu, Lugosi, Gabor +1 · 6 citations
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1509.05845

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.

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