One of the most basic problems in statistics is how to estimate the expected value of a distribution, based on a sample of independent random draws. When the goal is to minimize the length of a confidence interval, the usual empirical mean has a sub-optimal performance, especially for heavy-tailed distributions. In this talk we discuss some estimators that achieve a sub-Gaussian performance under general conditions. The multivariate scenario turns out to be more challenging. We present an estimator with near-optimal performance. We also discuss how these ideas extend to regression function estimation.

The talk is based on joint work with Shahar Mendelson (Technion, Israel), Luc Devroye (Mcgill University, Canada), Matthieu Lerasle (CNRS, France) and Roberto Imbuzeiro Oliveira (IMPA, Brazil).

*Gabor Lugosi is an ICREA Research Professor at the Pompeu Fabra University in Barcelona, Spain where he has been since 1996. He received his PhD in Electrical Engineering from the Hungarian Academy of Sciences in 1991. His research interests include the theory of machine learning, combinatorial statistics, inequalities in probability, random graphs and random structures, and information theory.*