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

2016/03/08 by Fengnan Gao, Gao, Fengnan, Aad van der Vaart +1
Mathematics · Physics and Astronomy · #62M05 #Complex Network Analysis Techniques #FOS: Mathematics #Opinion Dynamics and Social Influence #Random Matrices and Applications #Statistics Theory (math.ST) #math.ST #msc:62M05 #stat.TH

paper · pdf · doi:10.48550/arxiv.1603.02625

final version before acceptance in Stochastic Processes and Their Applications, 26 pages, 2 figures, 1 table

openalex publication_date 2016/03/08 · arxiv created 2017/03/08 · arxiv updated 2017/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Structure and Function of Complex Networks

Cited by

• Likelihood-based anomaly detection in preferential attachment networks

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