Given n independent, identically distributed copies of a random
vector, one is interested in estimating the expected value. Perhaps
surprisingly, there are still open questions concerning this very
basic problem in statistics. The goal is to construct estimators
that are close to the true mean with high probability, with respect to
some given norm. In this talk we are primarily interested
in non-asymptotic sub-Gaussian estimates. We introduce the
median-of-means tournament and show its optimal behavior.
This talk is based on joint work with Shahar Mendelson.