On the estimation of the mean of a random vector

Authors: Emilien Joly, Gábor Lugosi and

Electronic Journal of Statistics, Vol. 11, No 1, 440-451, April, 2017

We study the problem of estimating the mean of a multivariate distribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.