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Efficient estimation of covariance selection models


  • Frederick Wong


A Bayesian method is proposed for estimating an inverse covariance matrix from Gaussian data. The method is based on a prior that allows the off-diagonal elements of the inverse covariance matrix to be zero, and in many applications results in a parsimonious parameterisation of the covariance matrix. No assumption is made about the structure of the corresponding graphical model, so the method applies to both nondecomposable and decomposable graphs. All the parameters are estimated by model averaging using an efficient Metropolis--Hastings sampling scheme. A simulation study demonstrates that the method produces statistically efficient estimators of the covariance matrix, when the inverse covariance matrix is sparse. The methodology is illustrated by applying it to three examples that are high-dimensional relative to the sample size. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:809-830

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    Cited by:

    1. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
    2. Daye, Z. John & Jeng, X. Jessie, 2009. "Shrinkage and model selection with correlated variables via weighted fusion," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1284-1298, February.
    3. repec:bla:biomet:v:74:y:2018:i:1:p:185-195 is not listed on IDEAS
    4. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    5. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    6. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    7. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    8. Helen Armstrong & Christopher K. Carter & Kevin K. F. Wong & Robert Kohn, 2007. "Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models," Discussion Papers 2007-13, School of Economics, The University of New South Wales.
    9. Bai, Zhidong & Li, Hua & Wong, Wing-Keung, 2013. "The best estimation for high-dimensional Markowitz mean-variance optimization," MPRA Paper 43862, University Library of Munich, Germany.
    10. Pourahmadi, Mohsen & Wang, Xiao, 2015. "Distribution of random correlation matrices: Hyperspherical parameterization of the Cholesky factor," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 5-12.
    11. Dimitris Korobilis, 2013. "Var Forecasting Using Bayesian Variable Selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 204-230, March.
    12. David Chan & Robert Kohn & Chris Kirby, 2006. "Multivariate Stochastic Volatility Models with Correlated Errors," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 245-274.
    13. M Hashem Pesaran & Takashi Yamagata, 2012. "Testing CAPM with a Large Number of Assets," Discussion Papers 12/05, Department of Economics, University of York.
    14. Pesaran, M. H. & Yamagata, T., 2012. "Testing CAPM with a Large Number of Assets (Updated 28th March 2012)," Cambridge Working Papers in Economics 1210, Faculty of Economics, University of Cambridge.
    15. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    16. Donatello Telesca & Peter Müller & Steven M. Kornblau & Marc A. Suchard & Yuan Ji, 2012. "Modeling Protein Expression and Protein Signaling Pathways," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1372-1384, December.
    17. Fitch, A. Marie & Jones, Beatrix, 2012. "The cost of using decomposable Gaussian graphical models for computational convenience," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2430-2441.
    18. Michael Smith & Andrew Pitts, 2006. "Foreign Exchange Intervention by the Bank of Japan: Bayesian Analysis Using a Bivariate Stochastic Volatility Model," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 425-451.
    19. Zhidong Bai & Hua Li & Michael McAleer & Wing-Keung Wong, 2016. "Spectrally-corrected estimation for high-dimensional markowitz mean-variance optimization," Documentos de Trabajo del ICAE 2017-05, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    20. Carter, Christopher K. & Wong, Frederick & Kohn, Robert, 2011. "Constructing priors based on model size for nondecomposable Gaussian graphical models: A simulation based approach," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 871-883, May.
    21. Yu, Philip L.H. & Li, W.K. & Ng, F.C., 2014. "Formulating hypothetical scenarios in correlation stress testing via a Bayesian framework," The North American Journal of Economics and Finance, Elsevier, vol. 27(C), pages 17-33.
    22. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 130-140.
    23. repec:eee:regeco:v:70:y:2018:i:c:p:72-79 is not listed on IDEAS
    24. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.

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