IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i7p1525-1550.html
   My bibliography  Save this article

Robust Gaussian graphical modeling

Author

Listed:
  • Miyamura, Masashi
  • Kano, Yutaka

Abstract

A new Gaussian graphical modeling that is robustified against possible outliers is proposed. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its likelihood. Test statistics associated with the robustified estimators are developed. These include statistics for goodness of fit of a model. An outlying score, similar to but more robust than the Mahalanobis distance, is also proposed. The new scores make it easier to identify outlying observations. A Monte Carlo simulation and an analysis of a real data set show that the proposed method works better than ordinary Gaussian graphical modeling and some other robustified multivariate estimators.

Suggested Citation

  • Miyamura, Masashi & Kano, Yutaka, 2006. "Robust Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1525-1550, August.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1525-1550
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(06)00033-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    2. Nanny Wermuth & Eberhard Scheidt, 1977. "Fitting a Covariance Selection Model to a Matrix," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 88-92, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hokeun Sun & Hongzhe Li, 2012. "Robust Gaussian Graphical Modeling Via l 1 Penalization," Biometrics, The International Biometric Society, vol. 68(4), pages 1197-1206, December.
    2. Ahelegbey, Daniel Felix, 2015. "The Econometrics of Bayesian Graphical Models: A Review With Financial Application," MPRA Paper 92634, University Library of Munich, Germany, revised 25 Apr 2016.
    3. Hirose, Kei & Fujisawa, Hironori & Sese, Jun, 2017. "Robust sparse Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 172-190.
    4. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    5. Vinciotti, Veronica & Hashem, Hussein, 2013. "Robust methods for inferring sparse network structures," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 84-94.
    6. Stead, Alexander D. & Wheat, Phill & Greene, William H., 2023. "Robust maximum likelihood estimation of stochastic frontier models," European Journal of Operational Research, Elsevier, vol. 309(1), pages 188-201.
    7. Daniel Felix Ahelegbey, 2015. "The Econometrics of Networks: A Review," Working Papers 2015:13, Department of Economics, University of Venice "Ca' Foscari".

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. L. Alfaro & J. Fco. Ortega, 2009. "A comparison of robust alternatives to Hotelling's T2 control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(12), pages 1385-1396.
    2. Steffen Liebscher & Thomas Kirschstein, 2015. "Efficiency of the pMST and RDELA location and scatter estimators," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 63-82, January.
    3. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.
    4. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    5. Pokojovy, Michael & Jobe, J. Marcus, 2022. "A robust deterministic affine-equivariant algorithm for multivariate location and scatter," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    6. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466, April.
    7. Gervini, Daniel, 2003. "A robust and efficient adaptive reweighted estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 116-144, January.
    8. Sharifah Soaad Syed Yahaya & Hazlina Ali & Zurni Omar, 2011. "An Alternative Hotelling T^2 Control Chart Based on Minimum Vector Variance (MVV)," Modern Applied Science, Canadian Center of Science and Education, vol. 5(4), pages 132-132, August.
    9. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    10. Yunlu Jiang & Canhong Wen & Xueqin Wang, 2018. "Adaptive Exponential Power Depth with Application to Classification," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 466-480, October.
    11. Bhattacharya, Bhaskar, 2012. "Covariance selection and multivariate dependence," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 212-228.
    12. Zhu, Yongmeng & Wu, Jiechang & Wu, Jun & Liu, Shuyong, 2022. "Dimensionality reduce-based for remaining useful life prediction of machining tools with multisensor fusion," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    13. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.
    14. Marco Riani & Andrea Cerioli & Francesca Torti, 2014. "On consistency factors and efficiency of robust S-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 356-387, June.
    15. Taskinen, Sara & Croux, Christophe & Kankainen, Annaliisa & Ollila, Esa & Oja, Hannu, 2006. "Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 359-384, February.
    16. Fekri, M. & Ruiz-Gazen, A., 2004. "Robust weighted orthogonal regression in the errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 89-108, January.
    17. Juan Baz & Irene Díaz & Susana Montes & Raúl Pérez-Fernández, 2022. "Some results on the Gaussian Markov Random Field construction problem based on the use of invariant subgraphs," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 856-874, September.
    18. Ollila, Esa & Oja, Hannu & Croux, Christophe, 2003. "The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 328-355, November.
    19. Hardin, Johanna & Rocke, David M., 2004. "Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 625-638, January.
    20. Knox, Kris Joseph & Blankmeyer, Eric C. & Trinidad, José A. & Stutzman, J.R., 2009. "Predicting bankruptcy in the Texas nursing facility industry," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 1047-1064, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1525-1550. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.