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Article: Inference For The Degree Distributions Of Preferential Attachment Networks with zero-degree nodes

TitleInference For The Degree Distributions Of Preferential Attachment Networks with zero-degree nodes
Authors
KeywordsPreferential attachment with zero-degree nodes
Power-tail of degree distribution
Sylvester matrix equation
Martingale convergence theorem
Issue Date2020
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/jeconom
Citation
Journal of Econometrics, 2020, v. 216 n. 1, p. 220-234 How to Cite?
AbstractThe tail of the logarithmic degree distribution of networks decays linearly with respect to the logarithmic degree is known as the power law and is ubiquitous in daily lives. A commonly used technique in modeling the power law is preferential attachment (PA), which sequentially joins each new node to the existing nodes according to the conditional probability law proportional to a linear function of their degrees. Although effective, it is tricky to apply PA to real networks because the number of nodes and that of edges have to satisfy a linear constraint. This paper enables real application of PA by making each new node as an isolated node that attaches to other nodes according to PA scheme in some later epochs. This simple and novel strategy provides an additional degree of freedom to relax the aforementioned constraint to the observed data and uses the PA scheme to compute the implied proportion of the unobserved zero-degree nodes. By using martingale convergence theory, the degree distribution of the proposed model is shown to follow the power law and its asymptotic variance is proved to be the solution of a Sylvester matrix equation, a class of equations frequently found in the control theory (see Hansen and Sargent (2008, 2014)). These results give a strongly consistent estimator for the power-law parameter and its asymptotic normality. Note that this statistical inference procedure is non-iterative and is particularly applicable for big networks such as the World Wide Web presented in Section 6. Moreover, the proposed model offers a theoretically coherent framework that can be used to study other network features, such as clustering and connectedness, as given in Cheung (2016).
Persistent Identifierhttp://hdl.handle.net/10722/272342
ISSN
2019 Impact Factor: 1.577
2015 SCImago Journal Rankings: 3.781

 

DC FieldValueLanguage
dc.contributor.authorChan, NH-
dc.contributor.authorCheung, SKC-
dc.contributor.authorWong, SPS-
dc.date.accessioned2019-07-20T10:40:28Z-
dc.date.available2019-07-20T10:40:28Z-
dc.date.issued2020-
dc.identifier.citationJournal of Econometrics, 2020, v. 216 n. 1, p. 220-234-
dc.identifier.issn0304-4076-
dc.identifier.urihttp://hdl.handle.net/10722/272342-
dc.description.abstractThe tail of the logarithmic degree distribution of networks decays linearly with respect to the logarithmic degree is known as the power law and is ubiquitous in daily lives. A commonly used technique in modeling the power law is preferential attachment (PA), which sequentially joins each new node to the existing nodes according to the conditional probability law proportional to a linear function of their degrees. Although effective, it is tricky to apply PA to real networks because the number of nodes and that of edges have to satisfy a linear constraint. This paper enables real application of PA by making each new node as an isolated node that attaches to other nodes according to PA scheme in some later epochs. This simple and novel strategy provides an additional degree of freedom to relax the aforementioned constraint to the observed data and uses the PA scheme to compute the implied proportion of the unobserved zero-degree nodes. By using martingale convergence theory, the degree distribution of the proposed model is shown to follow the power law and its asymptotic variance is proved to be the solution of a Sylvester matrix equation, a class of equations frequently found in the control theory (see Hansen and Sargent (2008, 2014)). These results give a strongly consistent estimator for the power-law parameter and its asymptotic normality. Note that this statistical inference procedure is non-iterative and is particularly applicable for big networks such as the World Wide Web presented in Section 6. Moreover, the proposed model offers a theoretically coherent framework that can be used to study other network features, such as clustering and connectedness, as given in Cheung (2016).-
dc.languageeng-
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/jeconom-
dc.relation.ispartofJournal of Econometrics-
dc.subjectPreferential attachment with zero-degree nodes-
dc.subjectPower-tail of degree distribution-
dc.subjectSylvester matrix equation-
dc.subjectMartingale convergence theorem-
dc.titleInference For The Degree Distributions Of Preferential Attachment Networks with zero-degree nodes-
dc.typeArticle-
dc.identifier.emailCheung, SKC: simonkc@hku.hk-
dc.identifier.emailWong, SPS: sampwong@hku.hk-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jeconom.2020.01.015-
dc.identifier.scopuseid_2-s2.0-85079060288-
dc.identifier.hkuros298992-
dc.identifier.volume216-
dc.identifier.issue1-
dc.identifier.spage220-
dc.identifier.epage234-
dc.publisher.placeNetherlands-

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