I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating structural parameters of strategic network formation in economics and finance. Existing methods often produce unreliable estimates of parameters for the triangle, a key network structure that captures the tendency of two persons with shared friends to connect. Such unreliable estimates may lead to untrustworthy policy recommendations for networks with triangles. Through a variational mean-field approach, my algorithm addresses the two well-known difficulties when estimating the ERGM, the intractability of its normalizing constant and model degeneracy. In addition, I introduce l2 regularization that ensures a unique solution to the mean-field approximation problem under suitable conditions. I provide a non-asymptotic optimization convergence rate analysis for my proposed algorithm under mild regularity conditions. Through Monte Carlo simulations, I demonstrate that my method achieves 100% sign recovery rate for triangle parameters for small and mid-sized networks under perturbed initialization, compared to a 50% rate for existing algorithms. I provide the sensitivity analysis of estimates of ERGM parameters to hyperparameter choices, offering practical insights for implementation.

When I was in college, I used to listen to radio a lot. It was one of the habits I had before the bed. There was a radio program in Korea, “Radio Paradise.” The host of program was funny and had a good sense of music. The song I post is the opening song of the program. The program started at midnight sharp. Before the program started, there was always an announcement that alarms midnight. I started humming this song even before the announcement finished. What is he going to say as an opening comment today? What stories will make me smile today? Such imagination made me not able to sleep until the program ended, 02:00 am (Yes, I was quite a night-owl).

This paper introduces the Interference Sensitivity Model (ISM), a novel approach to assess the sensitivity of causal effects in network settings under unobserved confounding and partial interference, which allows for interactions within clusters but not across clusters. The ISM provides credible bounds for Average Direct Effects (ADE) and Average Spillover Effects (ASE) by maximizing a constrained geometric programming, which is a non-convex optimization problem.

This paper proposes a Distributionally Robust (DR) linear quantile estimator to handle deviations from the “Missing At Random” (MAR) assumption in incomplete data. While MAR-based estimators can perform poorly when the missingness mechanism deviates from MAR, fully assumption-free approaches yield overly conservative bounds. To address this, we introduce a distributionally robust optimization framework using the Wasserstein distance to measure departures from the MAR distribution. The estimator solves a minimax optimization problem by maximizing the worst-case expected loss over a Wasserstein ball and minimizing it with respect to the parameter of interest.