### Estimating the mean of a random vector

Probability Seminar

12th November 2021, 3:30 pm – 4:30 pm

Fry Building, 2.04 (also on Zoom)

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.

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