Mean estimation: median-of-means tournaments

Mean estimation: median-of-means tournaments

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Gábor Lugosi, ICREA & Pompeu Fabra University, Spain
Fine Hall 214

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).