Simultaneous inference for a high-dimensional precision matrix

Gaussian graphical models have been widely used for network data analysis. Although various methods exist for estimating the parameters, simultaneous inference is essential for graphical models. In this study, we propose a bootstrap procedure to conduct simultaneous inference for Gaussian graphical models. The simultaneous inference procedure is applied to large-scale graphical models and allows the dimension of the parameter vector of interest to exceed the sample size. We prove that the simultaneous test achieves a pre-set significance level asymptotically. Further simulation studies demonstrate the effectiveness of the proposed methods.