Recovering Model Structures from Large Low Rank and Sparse Covariance Matrix Estimation
AbstractMany 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1111.1133.
Date of creation: Nov 2011
Date of revision: Mar 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-14 (All new papers)
- NEP-CMP-2011-11-14 (Computational Economics)
- NEP-ECM-2011-11-14 (Econometrics)
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