Robust multivariate mean estimation: The optimality of trimmed mean

Authors: Gábor Lugosi and Shahar Mendelson

Annals of Statistics, Vol. 49, No 1, 393-410, February, 2021

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.