This paper introduces a general framework of covariance structures that can be verified in many popular statistical models, such as factor and random effect models. The new structure is a summation of low rank and sparse matrices. 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. The estimatoris computed efficiently using convex optimization. We propose an iterative algorithm , based on Nesterov's method, to solve the optimization criterion. The algorithm is shown to produce a solution within O(1/t^2) of the optimal, after any finite t iterations. Numerical performance is illustrated using simulated data and stock portfolio selection on S&P 100.
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. 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 sparsity patterns of these two components, and thus partially recovers the model structures . Convergence rates under various matrix norms are also presented. To compute this estimator, we further develop a first-order iterative algorithm to solve a convex optimization problem that contains separa- ble non-smooth functions, and the algorithm is shown to produce a solution within O(1/t^2) of the optimal, after any finite t iterations. Numerical performance is illustrated using simulated data and stock portfolio selection on S&P 100.
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This paper introduces a general framework of covariance structures that can be verified in many
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effect models. The new structure
effects models, give arise a certain type of covariance structures that
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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
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
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support of the two componentsrespectively
sparsity patterns of these two components, and thus partially recovers the model structures
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matrix
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The estimatoris computed efficiently using convex optimization. We propose an iterative algorithm , based on Nesterov's method, to solve the optimization criterion. The
To compute this estimator, we further develop a first-order iterative algorithm to solve a convex optimization problem that contains separa- ble non-smooth functions, and the