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March 2008 Sparse estimation of large covariance matrices via a nested Lasso penalty
Elizaveta Levina, Adam Rothman, Ji Zhu
Ann. Appl. Stat. 2(1): 245-263 (March 2008). DOI: 10.1214/07-AOAS139

Abstract

The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the bandwidth adaptively for each row of the Cholesky factor, using a novel penalty we call nested Lasso. This structure has more flexibility than regular banding, but, unlike regular Lasso applied to the entries of the Cholesky factor, results in a sparse estimator for the inverse of the covariance matrix. An iterative algorithm for solving the optimization problem is developed. The estimator is compared to a number of other covariance estimators and is shown to do best, both in simulations and on a real data example. Simulations show that the margin by which the estimator outperforms its competitors tends to increase with dimension.

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Elizaveta Levina. Adam Rothman. Ji Zhu. "Sparse estimation of large covariance matrices via a nested Lasso penalty." Ann. Appl. Stat. 2 (1) 245 - 263, March 2008. https://doi.org/10.1214/07-AOAS139

Information

Published: March 2008
First available in Project Euclid: 24 March 2008

zbMATH: 1137.62338
MathSciNet: MR2415602
Digital Object Identifier: 10.1214/07-AOAS139

Keywords: Cholesky decomposition , Covariance matrix , high dimension low sample size , large p small n , Lasso , Sparsity

Rights: Copyright © 2008 Institute of Mathematical Statistics

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