Sub-Gaussian Estimators of the Mean of a Random Vector

• Authors: Gábor Lugosi and Shahar Mendelson.
• Annals of Statistics, Vol. 47, No. 2, 783-794, February 2019.

We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median