Asymptotics in Undirected Random Graph Models Parameterized by the Strengths of Vertices

25 Pages Posted: 27 Jan 2015

See all articles by Ting Yan

Ting Yan

Central China Normal University

Hong Qin

Central China Normal University

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: January 26, 2015

Abstract

To capture the heterozygous of vertex degrees of networks and understand their distributions, a class of random graph models parameterized by the strengths of vertices, are proposed. These models are equipped in the framework of mutually independent edges, where the number of parameters matches with the size of networks. The asymptotic properties of the maximum likelihood estimator have been derived in some special models such as the β-model, but general results are lacking. In these models, the likelihood equations are identical to the moment equations. In this paper, we establish a unified asymptotic result including the consistency and asymptotic normality of the moment estimator instead of the maximum likelihood estimator, when the number of parameters goes to infinity. We apply it to the generalized β-model, maximum entropy models and Poisson models.

Keywords: Asymptotical Normality, Consistency, Moment Estimators, Increasing Number of Parameters, Undirected Random Graph Models

Suggested Citation

Yan, Ting and Qin, Hong and Wang, Hansheng, Asymptotics in Undirected Random Graph Models Parameterized by the Strengths of Vertices (January 26, 2015). Available at SSRN: https://ssrn.com/abstract=2555489 or http://dx.doi.org/10.2139/ssrn.2555489

Ting Yan

Central China Normal University ( email )

152 Luoyu Road
Wuhan, Hubei 430079
China

Hong Qin

Central China Normal University ( email )

152 Luoyu Road
Wuhan, Hubei 430079
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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