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It is well-known that trimmed sample means are robust against heavy tails anddata contamination. This paper analyzes the performance of trimmed means andrelated methods in two novel contexts. The first one consists of estimatingexpectations of functions in a given family, with uniform error bounds; this isclosely related to the problem of estimating the mean of a random vector undera general norm. The second problem considered is that of regression withquadratic loss. In both cases, trimmed-mean-based estimators are the first toobtain optimal dependence on the (adversarial) contamination level. Moreover,they also match or improve upon the state of the art in terms of heavy tails.Experiments with synthetic data show that a natural ``trimmed mean linearregression'' method often performs better than both ordinary least squares andalternative methods based on median-of-means.

Trimmed sample means for robust uniform mean estimation and regression