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Asymptotic normality in the maximum entropy models on graphs with an increasing number of parameters

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  • Yan, Ting
  • Zhao, Yunpeng
  • Qin, Hong

Abstract

Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the β-model to weighted graphs. Similar to the β-model, each vertex in maximum entropy models is assigned a potential parameter, and the degree sequence is the natural sufficient statistic. Hillar and Wibisono (2013) have proved the consistency of the maximum likelihood estimators. In this paper, we further establish the asymptotic normality for any finite number of the maximum likelihood estimators in the maximum entropy models with three types of edge weights, when the total number of parameters goes to infinity. Simulation studies are provided to illustrate the asymptotic results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:61-76
    DOI: 10.1016/j.jmva.2014.08.013
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    References listed on IDEAS

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    1. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    2. 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.
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    Cited by:

    1. 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.
    2. Han, Ruijian & Chen, Kani & Tan, Chunxi, 2020. "Bivariate gamma model," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    3. Jing Luo & Haoyu Wei & Xiaoyu Lei & Jiaxin Guo, 2021. "Asymptotic in a class of network models with an increasing sub-Gamma degree sequence," Papers 2111.01301, arXiv.org, revised Nov 2023.
    4. Zhao, Yunpeng, 2022. "Network inference from temporally dependent grouped observations," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    5. Yan, Ting, 2015. "A note on asymptotic distributions in maximum entropy models for networks," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 1-5.
    6. Jing Luo & Tour Liu & Qiuping Wang, 2022. "Affiliation weighted networks with a differentially private degree sequence," Statistical Papers, Springer, vol. 63(2), pages 367-395, April.
    7. Yong, Zhang & Chen, Siyu & Qin, Hong & Yan, Ting, 2016. "Directed weighted random graphs with an increasing bi-degree sequence," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 235-240.
    8. Yan, Ting & Zhao, Yunpeng, 2016. "Asymptotics of score test in the generalized β-model for networks," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 163-169.

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