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Application of fused graphical lasso to statistical inference for multiple sparse precision matrices

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  • Qiuyan Zhang
  • Lingrui Li
  • Hu Yang

Abstract

In this paper, the fused graphical lasso (FGL) method is used to estimate multiple precision matrices from multiple populations simultaneously. The lasso penalty in the FGL model is a restraint on sparsity of precision matrices, and a moderate penalty on the two precision matrices from distinct groups restrains the similar structure across multiple groups. In high-dimensional settings, an oracle inequality is provided for FGL estimators, which is necessary to establish the central limit law. We not only focus on point estimation of a precision matrix, but also work on hypothesis testing for a linear combination of the entries of multiple precision matrices. We apply a de-biasing technology, which is used to obtain a new consistent estimator with known distribution for implementing the statistical inference, and extend the statistical inference problem to multiple populations. The corresponding de-biasing FGL estimator and its asymptotic theory are provided. A simulation study and an application of the diffuse large B-cell lymphoma data show that the proposed test works well in high-dimensional situation.

Suggested Citation

  • Qiuyan Zhang & Lingrui Li & Hu Yang, 2024. "Application of fused graphical lasso to statistical inference for multiple sparse precision matrices," PLOS ONE, Public Library of Science, vol. 19(5), pages 1-26, May.
    • Handle: RePEc:plo:pone00:0304264
    DOI: 10.1371/journal.pone.0304264
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    References listed on IDEAS

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    1. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    2. Jana Janková & Sara Geer, 2017. "Honest confidence regions and optimality in high-dimensional precision matrix estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 143-162, March.
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