Mean estimation and regression under heavy-tailed distributions--a survey

We survey some of the recent advances in mean estimation and regression\nfunction estimation. In particular, we describe sub-Gaussian mean estimators\nfor possibly heavy-tailed data both in the univariate and multivariate\nsettings. We focus on estimators based on median-of-means techniques but other\nmethods such as the trimmed mean and Catoni's estimator are also reviewed. We\ngive detailed proofs for the cornerstone results. We dedicate a section on\nstatistical learning problems--in particular, regression function\nestimation--in the presence of possibly heavy-tailed data.\n