Normal Approximation in Large Network Models
Michael Leung and
Hyungsik Roger Moon
Papers from arXiv.org
We prove central limit theorems for models of network formation and network processes with homophilous agents. The results hold under large-network asymptotics, enabling inference in the typical setting where the sample consists of a small set of large networks. We first establish a general central limit theorem under high-level `stabilization' conditions that provide a useful formulation of weak dependence, particularly in models with strategic interactions. The result delivers a square root n rate of convergence and a closed-form expression for the asymptotic variance. Then using techniques in branching process theory, we derive primitive conditions for stabilization in the following applications: static and dynamic models of strategic network formation, network regressions, and treatment effects with network spillovers. Finally, we suggest some practical methods for inference.
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