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 | Rank | |
|---|---|---|---|---|
| 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 Error1.45e+3 | 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 |
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