2023/03/02 by Qiuyan Zhang, Zhidong Bai, Zhang, Qiuyan +5 · 1 citation
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2303.01326
openalex publication_date 2023/03/02 · openalex created_date 2023/03/05 · openalex updated_date 2026/07/28
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. Inspired by Jankova a and van de Geer [confidence intervals for high-dimensional inverse covariance estimation, Electron. J. Stat. 9(1) (2015) 1205-1229.], who investigated a de-biasing technology to obtain a new consistent estimator with known distribution for implementing the statistical inference, we extend the statistical inference problem to multiple populations, and propose the de-biasing FGL estimators. The corresponding asymptotic property of de-biasing FGL estimators is provided. A simulation study shows that the proposed test works well in high-dimensional situations.