Positive definite estimators of large covariance matrices

Adam J. Rothman

doi:10.1093/biomet/ass025

Positive definite estimators of large covariance matrices

Adam J. Rothman

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

93 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	733-740
Number of pages	8
Journal	Biometrika
Volume	99
Issue number	3
DOIs	https://doi.org/10.1093/biomet/ass025
State	Published - Sep 2012

Bibliographical note

Funding Information:
The author thanks the editor, associate editor, and referees for helpful suggestions, as well as Tiefeng Jiang for a helpful discussion. The author’s research is supported in part by a grant from the U.S. National Science Foundation.

Keywords

Barrier function
Classification
Convex optimization
High-dimensional data
Sparsity

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AB - 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.

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KW - Convex optimization

KW - High-dimensional data

KW - Sparsity

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ER -

Positive definite estimators of large covariance matrices

Abstract

Bibliographical note

Keywords

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