Positive-definite l1-penalized estimation of large covariance matrices

Lingzhou Xue, Shiqian Ma, Hui Zou

Research output: Contribution to journalArticlepeer-review

82 Scopus citations

Abstract

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite l1- penalized covariance estimator for estimating sparse large covariance matrices. We derive an efficient alternating direction method to solve the challenging optimization problem and establish its convergence properties. Under weak regularity conditions, nonasymptotic statistical theory is also established for the proposed estimator. The competitive finite-sample performance of our proposal is demonstrated by both simulation and real applications.

Original languageEnglish (US)
Pages (from-to)1480-1491
Number of pages12
JournalJournal of the American Statistical Association
Volume107
Issue number500
DOIs
StatePublished - Dec 1 2012

Keywords

  • Alternating direction methods
  • Matrix norm
  • Positive-definite estimation
  • Soft-thresholding
  • Sparsity

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