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arXiv · 1801.05565

Robust Modifications of U-statistics and Applications to Covariance Estimation Problems

Stanislav Minsker·Xiaohan Wei
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Abstract

Let $Y$ be a $d$-dimensional random vector with unknown mean $μ$ and covariance matrix $Σ$. This paper is motivated by the problem of designing an estimator of $Σ$ that admits tight deviation bounds in the operator norm under minimal assumptions on the underlying distribution, such as existence of only 4th moments of the coordinates of $Y$. To address this problem, we propose robust modifications of the operator-valued U-statistics, obtain non-asymptotic guarantees for their performance, and demonstrate the implications of these results to the covariance estimation problem under various structural assumptions.

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Stanislav Minsker, Xiaohan Wei. 2018-03-08. Robust Modifications of U-statistics and Applications to Covariance Estimation Problems. https://arxiv.org/abs/1801.05565

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