Statistics Papers

Document Type

Journal Article

Date of this Version

2011

Publication Source

Journal of the American Statistical Association

Volume

106

Issue

494

Start Page

594

Last Page

607

DOI

10.1198/jasa.2011.tm10155

Abstract

A constrained 1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of n iid p-variate random variables. The resulting estimator is shown to have a number of desirable properties. In particular, it is shown that the rate of convergence between the estimator and the true s-sparse precision matrix under the spectral norm is s√log p/n when the population distribution has either exponential-type tails or polynomial-type tails. Convergence rates under the elementwise norm and Frobenius norm are also presented. In addition, graphical model selection is considered. The procedure is easily implemented by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset. The procedure performs favorably in comparison to existing methods.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 24 Jan 2012, available online: http://wwww.tandfonline.com/10.1198/jasa.2011.tm10155.

Keywords

covariance matrix, Frobenius norm, Gaussian graphical model, precision matrix, rate of convergence, spectral norm

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Date Posted: 27 November 2017