# Improved covariance estimation: optimal robustness and sub-Gaussian guarantees under heavy tails

@inproceedings{Oliveira2022ImprovedCE, title={Improved covariance estimation: optimal robustness and sub-Gaussian guarantees under heavy tails}, author={Roberto I. Oliveira and Zoraida F. Rico}, year={2022} }

We present an estimator of the covariance matrix Σ of random d -dimensional vector from an i.i.d. sample of size n . Our sole assumption is that this vector satisﬁes a bounded L p − L 2 moment assumption over its one-dimensional marginals, for some p ≥ 4. Given this, we show that Σ can be estimated from the sample with the same high-probability error rates that the sample covariance matrix achieves in the case of Gaussian data. This holds even though we allow for very general distributions that…

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