Statistically Optimal Robust Mean and Covariance Estimation for Anisotropic Gaussians

Abstract

Assume that X 1 , . . . , X N is an ε-contaminated sample of N independent Gaussian vectors in R d with mean µ and covariance Σ. In the strong ε-contamination model we assume that the adversary replaced an ε fraction of vectors in the original Gaussian sample by any other vectors. We show that there is an estimator µ of the mean satisfying, with probability at least 1 − δ, a bound of the form