Positive definite estimators of large covariance matrices

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Using convex optimization, we construct a sparse estimator of the covariance matrix that is positive definite and performs well in high-dimensional settings. A lasso-type penalty is used to encourage sparsity and a logarithmic barrier function is used to enforce positive definiteness. Consistency and convergence rate bounds are established as both the number of variables and sample size diverge. An efficient computational algorithm is developed and the merits of the approach are illustrated with simulations and a speech signal classification example.

Original languageEnglish (US)
Pages (from-to)733-740
Number of pages8
Issue number3
StatePublished - Sep 1 2012


  • Barrier function
  • Classification
  • Convex optimization
  • High-dimensional data
  • Sparsity

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