Sparse Covariance Matrix Estimation With Eigenvalue Constraints

作者：Liu Han^*; Wang Lie; Zhao Tuo

来源：Journal of Computational and Graphical Statistics, 2014, 23(2): 439-459.

DOI：10.1080/10618600.2013.782818

• Explicit eigenvalue constraint
• High-dimensional data
• Positive-definiteness guarantee

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 mini-max 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.

• 出版日期2014-6