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Sparse Matrix Graphical Models

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  • Chenlei Leng
  • Cheng Yong Tang

Abstract

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information. In this article, we propose a novel sparse matrix graphical model for these types of statistical problems. By penalizing, respectively, two precision matrices corresponding to the rows and columns, our method yields a sparse matrix graphical model that synthetically characterizes the underlying conditional independence structure. Our model is more parsimonious and is practically more interpretable than the conventional sparse vector-variate graphical models. Asymptotic analysis shows that our penalized likelihood estimates enjoy better convergent rates than that of the vector-variate graphical model. The finite sample performance of the proposed method is illustrated via extensive simulation studies and several real datasets analysis.

Suggested Citation

  • Chenlei Leng & Cheng Yong Tang, 2012. "Sparse Matrix Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1187-1200, September.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1187-1200
    DOI: 10.1080/01621459.2012.706133
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    Cited by:

    1. repec:eee:econom:v:201:y:2017:i:2:p:176-197 is not listed on IDEAS
    2. Hafner, C. M. & Linton, O., 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," Cambridge Working Papers in Economics 1664, Faculty of Economics, University of Cambridge.
    3. repec:bla:biomet:v:73:y:2017:i:3:p:780-791 is not listed on IDEAS

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