Sub-Gaussian mean estimators

About

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.

Luc Devroye, Matthieu Lerasle, Gabor Lugosi, Roberto I. Oliveira · 2015

Related benchmarks

Task	Dataset	Result
Robust Covariance Estimation	Non-elliptical Laplace coordinates ε = 0.0	Covariance Error0.353	7
Covariance Estimation	Elliptical Gaussian (ε = 0.0) (synthetic)	Covariance Error0.374	7
Robust Covariance Estimation	Non-elliptical signed log-normal (sigma = 0.5) epsilon = 0.0	Covariance Error33.3	7
Robust Covariance Estimation	Elliptical Student-t df=8 epsilon = 0.0	CovErr0.419	7
Covariance Estimation	Elliptical Student-t df=8 contamination level ε = 0.05	Covariance Error9.27	7
Covariance Estimation	Elliptical Gaussian contamination level ε = 0.05	CovErr8.07	7
Covariance Estimation	Non-elliptical signed log-normal (σ = 0.5) with contamination level ε = 0.1 (test)	Covariance Error15.3	7
Robust Covariance Estimation	Non-elliptical Laplace coordinates contamination level ε = 0.1	Covariance Error1450	7
Robust Covariance Estimation	Elliptical Gaussian ε = 0.1	Covariance Error16.5	7
Robust Covariance Estimation	Elliptical Student-t contamination level ε = 0.1 df=8	Covariance Error16.4	7