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

Qiuyan Zhang, Lingrui Li and Hu Yang

PLOS ONE, 2024, vol. 19, issue 5, 1-26

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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0304264

DOI: 10.1371/journal.pone.0304264

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