High-dimensional semiparametric bigraphical models

Yang Ning, Han Liu

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)655-670
Number of pages16
Issue number3
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Bigraphical model
  • High dimensionality
  • Matrix-normal distribution
  • Rank-based statistic


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