A New Penalized Estimator for Sparse Inference in Gaussian Graphical Models: An Adaptive Non-Convex Approach

A new penalized estimator for sparse inference in Gaussian Graphical Models is proposed in this paper. It is based on the adaptive non-convex penalty function first presented in (4). In comparison to other estimators based on non-convex penalty functions, such as SCAD and MCP, the proposed estimator has a number of advantages because it allows controlling the degree of the non-convexity of the objective function through a second tuning parameter, which eliminates the inferential issues associated with the existence of multiple local minima. A simulation study is used to assess the proposed estimator's performance.