Normal Approximation in Large Network Models

2019-04-24

Social Science Research Network

AI Summary

This paper addresses asymptotic inference for a single large network sample generated by strategic interaction and homophily among agents in large-scale static and dynamic network formation models. To overcome the challenge of verifying conventional central limit theorems (CLTs) under network moment dependence, we adapt the exponential stabilization condition from stochastic geometry to network analysis—augmented by branching process theory—to derive verifiable primitive sufficient conditions. The resulting CLT framework requires no repeated sampling and applies directly to a single large network. It substantially broadens the theoretical foundation for network parameter estimation and hypothesis testing, and provides the first asymptotic normality guarantee for strategic network models with explicit, quantifiable regularity conditions.

Abstract

We develop a methodology for proving central limit theorems in network models with strategic interactions and homophilous agents. We consider an asymptotic framework in which the size of the network tends to infinity, which is useful for inference in the typical setting in which the sample consists of a single large network. In the presence of strategic interactions, network moments are generally complex functions of network components, where a node's component consists of all alters to which it is directly or indirectly connected. We find that a modification of "exponential stabilization" conditions from the stochastic geometry literature provides a useful formulation of weak dependence for moments of this type. Our first contribution is to prove a CLT for a large class of network moments satisfying stabilization and a moment condition. Our second contribution is a methodology for deriving primitive sufficient conditions for stabilization using results in branching process theory. We apply the methodology to static and dynamic models of network formation and discuss how it can be used more broadly.

Problem

• Proving central limit theorem for strategic network formation models
• Establishing weak dependence conditions via stabilization modification
• Deriving interpretable conditions restricting strategic interaction strength

Innovation

• Stabilization conditions for weak dependence
• Strategic interaction strength restrictions
• Branching process theory for conditions