A note on asymptotic distributions in directed exponential random graph models with bi-degree sequences

摘要

The asymptotic normality of a fixed number of the maximum likelihood estimators (MLEs) in the directed exponential random graph models with an increasing bi-degree sequence has been established recently. In this article, we further derive a central limit theorem for a linear combination of all the MLEs with an increasing dimension. Simulation studies are provided to illustrate the asymptotic results.