Improved covariance estimation: Optimal robustness and sub-Gaussian guarantees under heavy tails
改进的协方差估计：重尾下的最优稳健性与次高斯保证
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 Lp−L2 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…