A connection between Huber's contamination and heavy-tailed models yields unified robust mean estimators that are both computationally efficient and statistically optimal under certain conditions.
Sub-Gaussian estimators of the mean of a random vector
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abstract
We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of $X$ exists. The estimator is based on a novel concept of a multivariate median.
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A Unified Approach to Robust Mean Estimation
A connection between Huber's contamination and heavy-tailed models yields unified robust mean estimators that are both computationally efficient and statistically optimal under certain conditions.