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Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    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.

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