Estimation of Directed Acyclic Graphs by Frequentist Model Averaging

Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation remains challenging under graph structural uncertainty. We propose an optimal model averaging method for directed acyclic Gaussian graphs. With a set of candidate models varying by graph structures, we average estimates from candidate models using weights that minimize a penalized negative log-likelihood criterion. In contrast to existing approaches, we not only establish the asymptotic optimality, weight consistency, and parameter consistency of the proposed method, but also explicitly characterize how different candidate models affect the convergence rate. Moreover, we prove parameter consistency even when all candidate graph models are misspecified. Results from simulation studies and a real-data analysis on the banks' international liability data show the promise of the proposed method.