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arXiv · 1702.00482

Sub-Gaussian estimators of the mean of a random vector

Gábor Lugosi·Shahar Mendelson
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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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Gábor Lugosi, Shahar Mendelson. 2017-02-01. Sub-Gaussian estimators of the mean of a random vector. https://arxiv.org/abs/1702.00482

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