Should We Augment Large Covariance Matrix Estimation with Auxiliary Network Information?

In this paper, we propose two novel frameworks to incorporate auxiliary information about connectivity among entities (i.e., network information) into the estimation of large covariance matrices. The current literature either completely ignores this kind of network information (e.g., thresholding and shrinkage) or utilizes some simple network structure under very restrictive settings (e.g., banding). In the era of big data, we can easily get access to auxiliary information about the complex connectivity structure among entities. Depending on the features of the auxiliary network information at hand and the structure of the covariance matrix, we provide two different frameworks correspondingly —the Network Guided Thresholding and the Network Guided Banding. We show that both Network Guided estimators have optimal convergence rates over a larger class of sparse covariance matrix. Simulation studies demonstrate that they generally outperform other pure statistical methods, especially when the true covariance matrix is sparse, and the auxiliary network contains genuine information. Empirically, we apply our method to the estimation of the covariance matrix with the help of many financial linkage data of asset returns to attain the global minimum variance (GMV) portfolio.