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Estimation of a covariance matrix with zeros

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  • Sanjay Chaudhuri
  • Mathias Drton
  • Thomas S. Richardson

Abstract

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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    File URL: http://hdl.handle.net/10.1093/biomet/asm007
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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. Po-Hsien Huang & Hung Chen & Li-Jen Weng, 2017. "A Penalized Likelihood Method for Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 329-354, June.
    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. Michael Fop & Pierre-Alexandre Mattei & Charles Bouveyron & Thomas Brendan Murphy, 2022. "Unobserved classes and extra variables in high-dimensional discriminant analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 55-92, March.
    5. Bedoui, Adel & Lazar, Nicole A., 2020. "Bayesian empirical likelihood for ridge and lasso regressions," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    6. Alessandro Casa & Andrea Cappozzo & Michael Fop, 2022. "Group-Wise Shrinkage Estimation in Penalized Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 648-674, November.
    7. 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.
    8. 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.
    9. Lin Zhang & Andrew DiLernia & Karina Quevedo & Jazmin Camchong & Kelvin Lim & Wei Pan, 2021. "A random covariance model for bi‐level graphical modeling with application to resting‐state fMRI data," Biometrics, The International Biometric Society, vol. 77(4), pages 1385-1396, December.
    10. Anupam Kundu & Mohsen Pourahmadi, 2023. "MLE of Jointly Constrained Mean-Covariance of Multivariate Normal Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-32, May.
    11. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    12. Huimin Li & Jinru Wang, 2023. "Differentially Private Sparse Covariance Matrix Estimation under Lower-Bounded Moment Assumption," Mathematics, MDPI, vol. 11(17), pages 1-16, August.
    13. Felix Papier, 2016. "Supply Allocation Under Sequential Advance Demand Information," Operations Research, INFORMS, vol. 64(2), pages 341-361, April.
    14. Shojaie Ali & Michailidis George, 2010. "Network Enrichment Analysis in Complex Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-36, May.

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