Statistical Guarantees for Covariance Estimation with Adversarial Corruption under Constraints

We obtain a near-minimax rate on covariance estimation of adversarially corrupted Gaussian data in Frobenius norm when the covariance estimation is assumed to lie in a star-shaped set $K \subseteq \mathbb{R}^{n \times n}$. Assuming a known upper bound of $\varepsilon < 1/32$ on the fraction of the $