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Asymptotic theory in network models with covariates and a growing number of node parameters

Author

Listed:
  • Qiuping Wang

    (Zhaoqing University)

  • Yuan Zhang

    (The Ohio State University)

  • Ting Yan

    (Central China Normal University)

Abstract

We propose a general model that jointly characterizes degree heterogeneity and homophily in weighted, undirected networks. We present a moment estimation method using node degrees and homophily statistics. We establish consistency and asymptotic normality of our estimator using novel analysis. We apply our general framework to three applications, including both exponential family and non-exponential family models. Comprehensive numerical studies and a data example also demonstrate the usefulness of our method.

Suggested Citation

  • Qiuping Wang & Yuan Zhang & Ting Yan, 2023. "Asymptotic theory in network models with covariates and a growing number of node parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 369-392, April.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:2:d:10.1007_s10463-022-00848-0
    DOI: 10.1007/s10463-022-00848-0
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    References listed on IDEAS

    as
    1. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
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    4. Yan, Ting & Zhao, Yunpeng & Qin, Hong, 2015. "Asymptotic normality in the maximum entropy models on graphs with an increasing number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 61-76.
    5. Ting Yan & Binyan Jiang & Stephen E. Fienberg & Chenlei Leng, 2019. "Statistical Inference in a Directed Network Model With Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 857-868, April.
    6. Ting Yan & Jinfeng Xu, 2013. "A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices," Biometrika, Biometrika Trust, vol. 100(2), pages 519-524.
    7. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
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