Asymptotic theory in network models with covariates and a growing number of node parameters

TL;DR

This paper introduces a comprehensive asymptotic theory for network models that incorporate covariates and a growing number of node parameters, providing a unified estimation framework for complex network structures.

Contribution

It develops a general moment estimation method for weighted networks with degree heterogeneity and homophily, establishing its consistency and asymptotic normality, applicable to various model types.

Findings

Estimator is consistent and asymptotically normal.

Method performs well in numerical simulations.

Framework applies to both exponential and non-exponential family models.

Abstract

We propose a general model that jointly characterizes degree heterogeneity and homophily in weighted, undirected networks. We present a moment estimation method using node degrees and homophily statistics. We establish consistency and asymptotic normality of our estimator using novel analysis. We apply our general framework to three applications, including both exponential family and non-exponential family models. Comprehensive numerical studies and a data example also demonstrate the usefulness of our method.