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 in both 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 estimators are also reviewed. We give detailed proofs for the cornerstone results. We dedicate a section to statistical learning problems—in particular, regression function estimation—in the presence of possibly heavy-tailed data.

中文翻译：

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重尾分布下的均值估计和回归：一项调查

我们调查了均值估计和回归函数估计的一些最新进展。特别是，我们描述了单变量和多变量设置中可能存在重尾数据的次高斯均值估计量。我们将重点放在基于均值中值技术的估计量上，但是还将对其他方法（例如，均值和Catoni估计量）进行回顾。我们为基础结果提供了详细的证明。在可能存在大量尾部数据的情况下，我们专门讨论统计学习问题，尤其是回归函数估计。