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Estimation of a covariance matrix with zeros


  • Sanjay Chaudhuri
  • Mathias Drton
  • Thomas S. Richardson


We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm has guaranteed convergence properties. Dropping the assumption of multivariate normality, we show how to estimate the covariance matrix in an empirical likelihood approach. These approaches are then compared via simulation and on an example of gene expression. Copyright 2007, Oxford University Press.

Suggested Citation

  • Sanjay Chaudhuri & Mathias Drton & Thomas S. Richardson, 2007. "Estimation of a covariance matrix with zeros," Biometrika, Biometrika Trust, vol. 94(1), pages 199-216.
  • Handle: RePEc:oup:biomet:v:94:y:2007:i:1:p:199-216

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    References listed on IDEAS

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    Cited by:

    1. Natalia Bailey & Sean Holly & M. Hashem Pesaran, 2016. "A Two‐Stage Approach to Spatio‐Temporal Analysis with Strong and Weak Cross‐Sectional Dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 249-280, January.
    2. repec:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-017-9566-9 is not listed on IDEAS
    3. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    4. Ohlson, Martin & von Rosen, Dietrich, 2010. "Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1284-1295, May.
    5. Letchford, Adam N. & Nasiri, Saeideh D., 2015. "The Steiner travelling salesman problem with correlated costs," European Journal of Operational Research, Elsevier, vol. 245(1), pages 62-69.

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