Before revision:  We propose a LOw Rank and sparsE Covariance estimator (LOREC) to exploit this general structure in the high-dimensional setting. Analysis of this estimator shows that it recovers exactly the rank and support of the two componentsrespectively . Convergence rates under various  norms are also presented.
After revision:  This paper introduces a penalized approximation framework to recover such model structures from large covariance matrix estimation. We propose an estimator based on minimizing a non-likelihood loss with separable non-smooth penalty functions. This estimator is shown to recover exactly the rank and support of the two componentsrespectively . Convergence rates under various norms are also presented.