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.

Supported by the Spanish Ministry of Economy and Competitiveness Grant MTM2015-67304-P and FEDER, EU.