Sparse covariance matrix estimation with eigenvalue constraints

Han Liu, Lie Wang, Tuo Zhao

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)439-459
Number of pages21
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - Jan 1 2014


  • Explicit eigenvalue constraint; High-dimensional data; Positivedefiniteness guarantee

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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