Sub-Gaussian estimators of the mean of a random vector
Gábor Lugosi, Shahar Mendelson
The Annals of Statistics · 2019 · Volume 47 · Issue 2
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.
Keywords
60G25, 62G08, 62J02, Mean estimation, robust estimation, sub-Gaussian inequalities
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