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We consider the estimation of the affine parameter (and power-law exponent)in the preferential attachment model with random initial degrees. We derive thelikelihood, and show that the maximum likelihood estimator (MLE) isasymptotically normal and efficient. We also propose a quasi-maximum-likelihoodestimator (QMLE) to overcome the MLE's dependence on the history of the initialdegrees. To demonstrate the power of our idea, we present numericalsimulations.

On the Asymptotic Normality of Estimating the Affine Preferential Attachment Network Models with Random Initial Degrees