| In this era of rapid information development,research on data and the correlation between data is becoming more and more important.Among them,Gaussian graph model is a graph model method widely used in network data analysis.Now,there have been a lot of studies on the estimation methods of gaussian graph model parameters,and for these estimates,statistical inference methods based on the single point in the graph have also been gradually established.However,there are few researches on simultaneous inference of multiple points in Gaussian graph model,although this topic is also of great significance,this is because in practical applications,we tend to pay more attention to the connection of multiple points or a region in the network,rather than just between two points.In this paper,based on the simultaneous inference method of the generalized linear statistical model,combined with the existing parameter estimation and statistical inference methods of Gaussian graph model,we propose a bootstrap program for simultaneous statistical inference of the Gaussian graph model,including obtaining the simultaneous confidence region of multiple points in the graph model and the acceptance domain of hypothesis testing,and propose a method to deal with the support recovery problem.Our simultaneous inference method is suitable for large-scale graph models and allows the dimension of the concerned predictive variables to be larger than the sample size.Therefore,this method has good adaptability and extensibility.Moreover,we also prove theoretically that the simultaneous confidence region obtained by our method will asymptotically reach the predefined significance level,and the supporting recovery method is consistent and effective,and give the optimal separation parameters in theory.At the same time,we design a simulation experiment,through R language numerical simulation,the feasibility and effectiveness of this method in simultaneous statistical inference of Gaussian graph model are verified. |
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