Estimation of Directed Acyclic Graphs by Frequentist Model Averaging

2026-05-25

AI Summary

This work proposes a frequentist model averaging approach for estimating directed acyclic Gaussian graphical models under structural uncertainty. The method assigns weights to candidate DAG models by minimizing a penalized negative log-likelihood criterion. Theoretical analysis establishes, for the first time, the asymptotic optimality, weight consistency, and parameter consistency of the proposed estimator, and further reveals how the choice of candidate models influences the convergence rate. Notably, parameter consistency is guaranteed even when all candidate models are misspecified. Extensive simulations and an empirical application to international interbank liability data demonstrate that the proposed method substantially outperforms existing approaches in both estimation accuracy and robustness.

Abstract

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.

Problem

• Directed Acyclic Graphs
• Structural Uncertainty
• Model Averaging
• Graph Estimation
• Multivariate Network Data

Innovation

• model averaging
• directed acyclic graphs
• graph structural uncertainty
• parameter consistency
• penalized likelihood