Optimal rates of convergence for covariance matrix estimation

Understand

Covariance matrix plays a central role in multivariate statistical analysis.

• Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices.
• However, a minimax theory has yet been developed.
• In this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and Frobenius norm.