We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal conditions.
"Robust multivariate mean estimation: The optimality of trimmed mean." Ann. Statist. 49 (1) 393 - 410, February 2021. https://doi.org/10.1214/20-AOS1961