How to estimate the mean of a random variable?
Given n independent, identically distributed copies of a
random variable, one is interested in estimating the expected value.
Perhaps surprisingly, there are still open questions concerning this
very basic problem in statistics. In this talk we are primarily
interested in non-asymptotic sub-Gaussian estimates for potentially
heavy-tailed random variables. We discuss various estimates and
extensions to high dimensions. We apply the estimates for
statistical learning and regression function estimation problems.
The methods improve on classical empirical minimization techniques.
This talk is based on joint work with Emilien Joly, Luc Devroye,
Matthieu Lerasle, Roberto Imbuzeiro Oliveira, and Shahar Mendelson.