Uniform bounds for robust mean estimators
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Median-of-means technique is an elegant and general method for estimating the expectation of a random variable that provides strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. We consider generalizations of the median-of-means estimator that are based on ideas bridging the notions of symmetry and robustness. Next, we study deviations of the supremum of the stochastic process defined by these estimators, and prove new results that improve upon previously known bounds. Finally, implications of these results to the multivariate mean estimation problem are discussed.
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