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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.|
|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|
|Pages:||439 - 459|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Journal of Computational and Graphical Statistics|
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