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High-dimensional semiparametric bigraphical models

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  • Yang Ning
  • Han Liu

Abstract

In multivariate analysis, a Gaussian bigraphical model is commonly used for modelling matrix-valued data. In this paper, we propose a semiparametric extension of the Gaussian bigraphical model, called the nonparanormal bigraphical model. A projected nonparametric rank-based regularization approach is employed to estimate sparse precision matrices and produce graphs under a penalized likelihood framework. Theoretically, our semiparametric procedure achieves the parametric rates of convergence for both matrix estimation and graph recovery. Empirically, our approach outperforms the parametric Gaussian model for non-Gaussian data and is competitive with its parametric counterpart for Gaussian data. Extensions to the categorical bigraphical model and the missing data problem are discussed. Copyright 2013, Oxford University Press.

Suggested Citation

  • Yang Ning & Han Liu, 2013. "High-dimensional semiparametric bigraphical models," Biometrika, Biometrika Trust, vol. 100(3), pages 655-670.
  • Handle: RePEc:oup:biomet:v:100:y:2013:i:3:p:655-670
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    File URL: http://hdl.handle.net/10.1093/biomet/ast009
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    Cited by:

    1. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    2. HAFNER, Christian & LINTON, Oliver B. & TANG, Haihan, 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," LIDAM Discussion Papers CORE 2016044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    4. Jiadong Ji & Yong He & Lei Liu & Lei Xie, 2021. "Brain connectivity alteration detection via matrix‐variate differential network model," Biometrics, The International Biometric Society, vol. 77(4), pages 1409-1421, December.
    5. Anestis Touloumis & Simon Tavaré & John C. Marioni, 2015. "Testing the mean matrix in high-dimensional transposable data," Biometrics, The International Biometric Society, vol. 71(1), pages 157-166, March.

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