Title: Concentration for robust mean estimators: Some recent results
Authors: Emilien Joly - CIMAT (Mexico) [presenting]
Abstract: The estimation of the mean is a crucial step in many statistical contexts. Huber's work on the study of the asymptotic behavior of robust estimators in the context of heavy tailed random variables has recently been revisited. New robust estimators have been proposed that satisfy concentration inequalities hence at finite and fixed $n$ with sub-Gaussian speed under a small moment assumption (finite variance). The robust estimation of the mean for real valued random variables is a starting point for extensions of robust estimators to more complex probability fields. The focus will be on the definition of a robust estimator and its concentration in the case of vector valued distributions.