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 introduce a new family of estimators--the
so-called “median-of-means tournaments”---and show their optimal behavior.
This talk is based on joint work with Shahar Mendelson