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

Gabor Lugosi; Shahar Mendelson

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arXiv · 1906.04280

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

Gabor Lugosi·Shahar Mendelson

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Abstract

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

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math.ST cs.LG stat.ML stat.TH

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Gabor Lugosi, Shahar Mendelson. 2019-06-10. Mean estimation and regression under heavy-tailed distributions--a survey. https://arxiv.org/abs/1906.04280

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