Model selection for penalized Gaussian Graphical Models

High-dimensional data refers to the case in which the number of parameters is of one or more order greater than the sample size. Penalized Gaussian graphical models can be used to estimate the conditional independence graph in high-dimensional setting. In this setting, the crucial issue is to select the tuning parameter which regulates the sparsity of the graph. In this paper, we focus on estimating the "best" tuning parameter. We propose to select this tuning parameter by minimizing an information criterion based on the generalized information criterion and to use a stability selection approach in order to obtain a more stable graph. The performance of our method is compared with the state-of-art model selection procedures, including Akaike information criterion and Bayesian information criterion. A simulation study shows that our method performs better than the AIC, BIC.