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Sparse Covariance Matrix Estimation With Eigenvalue Constraints

Author(s): Liu, Han; Wang, Lie; Zhao, Tuo

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Abstract: We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online.
Publication Date: 2014
Citation: Liu, Han, Lie Wang, and Tuo Zhao. "Sparse covariance matrix estimation with eigenvalue constraints." Journal of Computational and Graphical Statistics 23, no. 2 (2014): 439-459. doi:10.1080/10618600.2013.782818
DOI: doi:10.1080/10618600.2013.782818
ISSN: 1061-8600
EISSN: 1537-2715
Pages: 439 - 459
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Computational and Graphical Statistics
Version: Author's manuscript

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