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arXiv · 1806.06233

Near-optimal mean estimators with respect to general norms

Gábor Lugosi·Shahar Mendelson
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Abstract

We study the problem of estimating the mean of a random vector in $\mathbb{R}^d$ based on an i.i.d.\ sample, when the accuracy of the estimator is measured by a general norm on $\mathbb{R}^d$. We construct an estimator (that depends on the norm) that achieves an essentially optimal accuracy/confidence tradeoff under the only assumption that the random vector has a well-defined covariance matrix. The estimator is based on the construction of a uniform median-of-means estimator in a class of real valued functions that may be of independent interest.

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Gábor Lugosi, Shahar Mendelson. 2018-06-16. Near-optimal mean estimators with respect to general norms. https://arxiv.org/abs/1806.06233

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