Sub-Gaussian estimators of the mean of a random vector
arXiv:1702.00482v1189 citations
Originality Highly original
AI Analysis
This provides a robust statistical method for mean estimation in high-dimensional or heavy-tailed data scenarios, with incremental improvements in theoretical guarantees.
The paper tackles the problem of estimating the mean of a random vector with only a second moment condition, introducing a new estimator based on a multivariate median that achieves purely sub-Gaussian performance.
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.