Estimation of Covariance Matrices under Sparsity Constraints

Abstract

We prove optimal sparsity oracle inequalities for the estimation of covariance matrix under the Frobenius norm. In particular we explore various sparsity structures on the underlying matrix.

This paper is part of a discussion of the paper "Minimax Estimation of Large Covariance Matrices under L1-Norm" by Tony Cai and Harrison Zhou, to appear in Statistica Sinica