Quebec Mathematical Sciences Colloquium

November 12, 2021 from 15:30 to 16:30 (Montreal/EST time)

Estimating the mean of a random vector

Colloquium presented by Gabor Lugosi (ICREA-UPF and BSE)

One of the most basic problems in statistics is the estimation of the mean of a random vector, based on independent observations. This problem has received renewed attention in the last few years, both from statistical and computational points of view. In this talk, we review some recent results on the statistical performance of mean estimators that allow heavy tails and adversarial contamination in the data. In particular, we are interested in estimators that have a near-optimal error in all directions in which the variance of the one dimensional marginal of the random vector is not too small. The material of this talk is based on a series of joint papers with Shahar Mendelson.