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

2019/06/10 by Gábor Lugosi, Shahar Mendelson, Lugosi, Gabor +1 · 17 citations
Mathematics · Computer Science · #Statistical Methods and Inference #Bayesian Methods and Mixture Models #Advanced Statistical Methods and Models

paper · pdf · doi:10.48550/arxiv.1906.04280

Abstract

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

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