On Estimating the Mean of a Random Vector

Abstract:

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. The basic punchline is that one can construct estimators that, under minimal conditions, achieve the same kind of performance as if the data was Gaussian. The material of this talk is based on a series of joint papers with Shahar Mendelson.

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Bio:

Gabor Lugosi is an ICREA research professor at the Department of Economics, Pompeu Fabra University, Barcelona. His research main interests include the theory of machine learning,  combinatorial statistics, inequalities in probability, random graphs and random structures, and information theory.