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.

翻译：有向无环图为表示多元网络数据中的有向依赖关系提供了基础工具，并被广泛应用于金融和经济网络的建模。然而，在图结构不确定的情况下，准确且可解释的估计仍然面临挑战。我们提出了一种针对有向无环高斯图的最优模型平均方法。给定一组图结构各异的候选模型，我们通过最小化惩罚负对数似然准则的权重对候选模型的估计进行平均。与现有方法相比，我们不仅建立了所提方法的渐近最优性、权重一致性和参数一致性，还明确刻画了不同候选模型如何影响收敛速度。此外，即使所有候选图模型设定错误，我们也证明了参数一致性。仿真研究以及对银行国际负债数据的实证分析结果表明，所提方法具有良好性能。