IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v69y2015i4p419-441.html
   My bibliography  Save this article

Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm

Author

Listed:
  • Fentaw Abegaz
  • Ernst Wit

Abstract

type="main" xml:id="stan12066-abs-0001"> Typical data that arise from surveys, experiments, and observational studies include continuous and discrete variables. In this article, we study the interdependence among a mixed (continuous, count, ordered categorical, and binary) set of variables via graphical models. We propose an ℓ 1 -penalized extended rank likelihood with an ascent Monte Carlo expectation maximization approach for the copula Gaussian graphical models and establish near conditional independence relations and zero elements of a precision matrix. In particular, we focus on high-dimensional inference where the number of observations are in the same order or less than the number of variables under consideration. To illustrate how to infer networks for mixed variables through conditional independence, we consider two datasets: one in the area of sports and the other concerning breast cancer.

Suggested Citation

  • Fentaw Abegaz & Ernst Wit, 2015. "Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 419-441, November.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:4:p:419-441
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/stan.12066
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Baker, Rose D. & McHale, Ian G., 2013. "Forecasting exact scores in National Football League games," International Journal of Forecasting, Elsevier, vol. 29(1), pages 122-130.
    2. repec:taf:jnlasa:v:108:y:2013:i:502:p:656-665 is not listed on IDEAS
    3. D. R. Cox & Nanny Wermuth, 1999. "Likelihood Factorizations for Mixed Discrete and Continuous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 209-220, June.
    4. 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.
    5. Boulier, Bryan L. & Stekler, H. O., 2003. "Predicting the outcomes of National Football League games," International Journal of Forecasting, Elsevier, vol. 19(2), pages 257-270.
    6. Brian S. Caffo & Wolfgang Jank & Galin L. Jones, 2005. "Ascent‐based Monte Carlo expectation– maximization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 235-251, April.
    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. Luigi Augugliaro & Veronica Vinciotti & Ernst C. Wit, 2022. "Extending graphical models for applications: on covariates, missingness and normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 241-251, June.
    2. Katerina Rigana & Ernst C. Wit & Samantha Cook, 2024. "Navigating Market Turbulence: Insights from Causal Network Contagion Value at Risk," Papers 2402.06032, arXiv.org.
    3. Abdolreza Mohammadi & Fentaw Abegaz & Edwin Heuvel & Ernst C. Wit, 2017. "Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(3), pages 629-645, April.

    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. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Papers 1910.13960, arXiv.org, revised Oct 2020.
    2. Vaughan Williams, Leighton & Stekler, Herman O., 2010. "Sports forecasting," International Journal of Forecasting, Elsevier, vol. 26(3), pages 445-447, July.
      • Herman O. Stekler, 2007. "Sports Forecasting," Working Papers 2007-001, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting, revised Jan 2007.
    3. Bing-Yi Jing & Zhouping Li & Guangming Pan & Wang Zhou, 2016. "On SURE-Type Double Shrinkage Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1696-1704, October.
    4. Benjamin Poignard & Manabu Asai, 2023. "Estimation of high-dimensional vector autoregression via sparse precision matrix," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 307-326.
    5. Mardi Dungey & Marius Matei & Matteo Luciani & David Veredas, 2017. "Surfing through the GFC: Systemic Risk in Australia," The Economic Record, The Economic Society of Australia, vol. 93(300), pages 1-19, March.
    6. Yue, Chen & Chen, Shaojie & Sair, Haris I. & Airan, Raag & Caffo, Brian S., 2015. "Estimating a graphical intra-class correlation coefficient (GICC) using multivariate probit-linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 126-133.
    7. Clifford Lam & Phoenix Feng & Charlie Hu, 2017. "Nonlinear shrinkage estimation of large integrated covariance matrices," Biometrika, Biometrika Trust, vol. 104(2), pages 481-488.
    8. Kamil Jurczak, 2018. "Weak Convergence of the Empirical Spectral Distribution of High-Dimensional Band Sample Covariance Matrices," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1273-1302, September.
    9. Bryan Boulier & H. O. Stekler & Sarah Amundson, 2006. "Testing the efficiency of the National Football League betting market," Applied Economics, Taylor & Francis Journals, vol. 38(3), pages 279-284.
    10. Huangdi Yi & Qingzhao Zhang & Cunjie Lin & Shuangge Ma, 2022. "Information‐incorporated Gaussian graphical model for gene expression data," Biometrics, The International Biometric Society, vol. 78(2), pages 512-523, June.
    11. Stekler, H.O. & Sendor, David & Verlander, Richard, 2010. "Issues in sports forecasting," International Journal of Forecasting, Elsevier, vol. 26(3), pages 606-621, July.
      • Herman O. Stekler & David Sendor & Richard Verlander, 2009. "Issues in Sports Forecasting," Working Papers 2009-002, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    12. Baker, Rose D. & McHale, Ian G., 2013. "Forecasting exact scores in National Football League games," International Journal of Forecasting, Elsevier, vol. 29(1), pages 122-130.
    13. Lidan Tan & Khai X. Chiong & Hyungsik Roger Moon, 2018. "Estimation of High-Dimensional Seemingly Unrelated Regression Models," Papers 1811.05567, arXiv.org.
    14. S Klaassen & J Kueck & M Spindler & V Chernozhukov, 2023. "Uniform inference in high-dimensional Gaussian graphical models," Biometrika, Biometrika Trust, vol. 110(1), pages 51-68.
    15. Qiang Sun & Hongtu Zhu & Yufeng Liu & Joseph G. Ibrahim, 2015. "SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 289-302, March.
    16. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    17. Luo, Shan & Chen, Zehua, 2014. "Edge detection in sparse Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 138-152.
    18. Nancy Ammon Jianakoplos & Martin Shields, 2012. "Practice or Profits," Journal of Sports Economics, , vol. 13(4), pages 451-465, August.
    19. Jingying Yang, 2024. "Element Aggregation for Estimation of High-Dimensional Covariance Matrices," Mathematics, MDPI, vol. 12(7), pages 1-16, March.
    20. Hubáček, Ondřej & Šír, Gustav, 2023. "Beating the market with a bad predictive model," International Journal of Forecasting, Elsevier, vol. 39(2), pages 691-719.

    More about this item

    Statistics

    Access and download statistics

    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:bla:stanee:v:69:y:2015:i:4:p:419-441. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.