A central limit theorem in the $\beta$-model for undirected random graphs with a diverging number of vertices

TL;DR

This paper proves a central limit theorem for the maximum likelihood estimator in the $eta$-model of undirected random graphs with a diverging number of vertices, extending previous consistency results.

Contribution

It derives the asymptotic normality of the MLE in the $eta$-model by approximating the inverse Fisher information matrix, under mild conditions.

Findings

Asymptotic normality of the MLE established

Simulation studies confirm theoretical results

Data example illustrates practical applicability

Abstract

Chatterjee, Diaconis and Sly (2011) recently established the consistency of the maximum likelihood estimate in the $\beta$-model when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we obtain its asymptotic normality under mild conditions. Simulation studies and a data example illustrate the theoretical results.