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, April, 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