  The preferential attachment (PA) model is a popular way of modeling dynamic
social networks, such as collaboration networks. Assuming that the PA function
takes a parametric form, we propose and study the maximum likelihood estimator
of the parameter. Using a supercritical continuous-time branching process
framework, we prove the almost sure consistency and asymptotic normality of
this estimator. We also provide an estimator that only depends on the final
snapshot of the network and prove its consistency, and its asymptotic normality
under general conditions. We compare the performance of the estimators to a
nonparametric estimator in a small simulation study.
