A central limit theorem in the  -model for undirected random graphs with a diverging number of vertices

Yan, Ting; Xu, Jinfeng

doi:10.1093/biomet/ass084

Cited by 90 publications

(68 citation statements)

References 9 publications

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“…The next lemma, which is due to Yan and Xu (2013), shows that −H −1 N AA is wellapproximated by Q N (see also Simons and Yao (1998)). PROOF: See Proposition A.1 of Yan and Xu (2013).…”

Section: Qedmentioning

confidence: 91%

An Econometric Model of Network Formation With Degree Heterogeneity

Graham¹

2017

Econometrica

198

164

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I introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent‐level heterogeneity in link surplus (degree heterogeneity). Like in fixed effects panel data analyses, the joint distribution of observed and unobserved agent‐level characteristics is left unrestricted. Two estimators for the (common) homophily parameter, β0, are developed and their properties studied under an asymptotic sequence involving a single network growing large. The first, tetrad logit (TL), estimator conditions on a sufficient statistic for the degree heterogeneity. The second, joint maximum likelihood (JML), estimator treats the degree heterogeneity {Ai0}i = 1N as additional (incidental) parameters to be estimated. The TL estimate is consistent under both sparse and dense graph sequences, whereas consistency of the JML estimate is shown only under dense graph sequences.

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“…The next lemma, which is due to Yan and Xu (2013), shows that −H −1 N AA is wellapproximated by Q N (see also Simons and Yao (1998)). PROOF: See Proposition A.1 of Yan and Xu (2013).…”

Section: Qedmentioning

confidence: 91%

An Econometric Model of Network Formation With Degree Heterogeneity

Graham¹

2017

Econometrica

198

164

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“…In the absence of covariates, its MLE large sample properties (for dense networks) are analyzed by Chatterjee, Diaconis, and Sly (2011) and Yan and Xu (2013), who call it the β-model. In this case, the distinction between "sender productivity" and "receiver attractiveness" for a given node disappears, but the parameters α i can be interpreted as the proclivity by node 35 Hoff (2005) parameterized the correlation between α out i and α in i , whereas Dzemski (2014) can allow for more general dependencies.…”

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confidence: 99%

Econometrics of network models

Paula¹

2016

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In this article I provide a (selective) review of the recent econometric literature on networks. I start with a discussion of developments in the econometrics of group interactions. I subsequently provide a description of statistical and econometric models for network formation and approaches for the joint determination of networks and interactions mediated through those networks. Finally, I give a very brief discussion of measurement issues in both outcomes and networks. My focus is on identification and computational issues, but estimation aspects are also discussed.

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“…Assuming that a unique ML solution exists and that N ij = 1 for all i = j, geometrically fast convergence to the fixed point was shown in [16] and [25]. Conditions for the asymptotic normality of the ML estimator when n tends to infinity and N ij = 1 for all i = j were presented in [26]. Necessary and sufficient conditions for the existence of a finite ML estimate were presented in [14], [25], and [27].…”

Section: A the Undirected β-Modelmentioning

confidence: 99%

The $\beta$-Model—Maximum Likelihood, Cramér–Rao Bounds, and Hypothesis Testing

Wahlström¹,

Skog²,

Rosa³

et al. 2017

IEEE Trans. Signal Process.

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Abstract-We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known β-model for random graphs by replacing the constant model parameters with regression functions. Cramér-Rao bounds are derived for the undirected β-model, the directed β-model, and the generalized β-model. The corresponding maximum likelihood estimators are compared to the bounds by means of simulations. Moreover, examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance. Last, the applicability of the model is demonstrated using dynamic social network data describing communication among healthcare workers.

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A central limit theorem in the -model for undirected random graphs with a diverging number of vertices

Cited by 90 publications

References 9 publications

An Econometric Model of Network Formation With Degree Heterogeneity

An Econometric Model of Network Formation With Degree Heterogeneity

Econometrics of network models

The $\beta$-Model—Maximum Likelihood, Cramér–Rao Bounds, and Hypothesis Testing

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