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Activity Number:
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190
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Type:
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Contributed
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Date/Time:
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Monday, August 4, 2008 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #301822 |
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Title:
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Large Gaussian Covariance Matrix Estimation with Markov Structure
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Author(s):
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Xinwei Deng*+ and Ming Yuan
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Companies:
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Georgia Institute of Technology and Georgia Institute of Technology
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Address:
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765 Ferst Drive NW, Atlanta, GA, 30332,
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Keywords:
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Covariance matrix ; Markov structure ; Sparsity ; Shrinkage estimators ; Semi-definite program
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Abstract:
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Covariance matrix estimation for a large number of Gaussian random variables is a challenging yet increasingly common problem. A fact neglected in practice is that the random variables are frequently observed with certain temporal or spatial structures. Such a problem arises naturally in many situations with time series and images as the most popular and important examples. In this paper, we propose shrinkage estimators of the covariance matrix specifically to address this issue. The proposed methods exploit sparsity in the inverse covariance matrix in a systematic fashion so that the estimate conforms with models of Markov structure and amenable for subsequent stochastic modeling. We show that the estimation procedure can be formulated as a semi-definite program and efficiently computed. We illustrate the merits of these methods through simulation and a real data example.
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