Application of fused graphical lasso to statistical inference for multiple sparse precision matrices
Qiuyan Zhang, Lingrui Li, Hu Yang, Debo Cheng, Debo Cheng, Debo Cheng
TL;DR
This paper introduces a statistical method to estimate and test relationships in data from multiple groups, using a technique called fused graphical lasso.
Contribution
The novel contribution is extending fused graphical lasso for statistical inference across multiple sparse precision matrices with a de-biasing technique.
Findings
The fused graphical lasso estimator satisfies an oracle inequality in high-dimensional settings.
A de-biasing method enables hypothesis testing for linear combinations of precision matrix entries across groups.
Simulation and real data applications show the method performs well in high-dimensional scenarios.
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…
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Taxonomy
TopicsStatistical Methods and Inference · Statistical Methods and Bayesian Inference · Bayesian Methods and Mixture Models