On the Asymptotic Normality of Estimating the Affine Preferential   Attachment Network Models with Random Initial Degrees
  We consider the estimation of the affine parameter (and power-law exponent) in the preferential attachment model with random initial degrees. We derive the likelihood, and show that the maximum likelihood estimator (MLE) is asymptotically normal and efficient. We also propose a quasi-maximum-likelihood estimator (QMLE) to overcome the MLE's dependence on the history of the initial degrees. To demonstrate the power of our idea, we present numerical simulations. 
Fengnan Gao, Aad van der Vaart
math.ST stat.TH