JSM 2011 Online Program

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Abstract Details

Activity Number: 526
Type: Contributed
Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract - #302837
Title: Condition Number Regularized Convariance Estimation
Author(s): Joong-Ho Won*+
Companies: VAPAHCS
Address: , , ,
Keywords: covariance matrix ; convex optimization ; regularization ; condition number
Abstract:

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. Several approaches to regularize high-dimensional covariance estimates have been proposed in the "large p small n" setting. In many applications, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with an explicit constraint on the condition number, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path.


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