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

TL;DR

This paper establishes the asymptotic normality and efficiency of estimators for the affine parameter in preferential attachment models with random initial degrees, introducing a quasi-MLE to improve practical applicability.

Contribution

It derives the likelihood for the model, proves the asymptotic properties of the MLE, and proposes a QMLE that is less dependent on initial degree history.

Findings

MLE is asymptotically normal and efficient

QMLE overcomes dependence on initial degree history

Numerical simulations demonstrate estimator performance

Abstract

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.