Title: Sub-Gaussian estimators of the mean of a random vector,
Abstract: 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.