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Sub-Gaussian Mean Estimators
April 1, 2016 @ 11:00 am - 12:00 pm
Roberto Oliveira (IMPA)
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. These results are in http://arxiv.org/abs/1509.05845, to appear in Ann Stat. (Joint work with L. Devroye, M. Lerasle, and G. Lugosi.)