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Positive definite estimators of large covariance matrices. (English) Zbl 1437.62595
Summary: 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.

62P10 Applications of statistics to biology and medical sciences; meta analysis
62H12 Estimation in multivariate analysis
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