Asymptotics in a probit model for directed networks

Abstract

In this paper, we use the probit distribution to model the degree heterogeneity of the directed networks. We refer this model as the Probit Network Model, in which each edge is independently distributed as a Bernoulli random variable with a success probability measured by the probit function with a set of degree parameters. By using the moment equation to estimate the degree parameters, we establish the uniform consistency and the asymptotic normality of the moment estimator when the number of nodes goes to infinity. Simulation studies are provided to illustrate the asymptotic results.

Keywords:

• Asymptotical normality
• consistency
• directed networks
• moment estimators
• probit model