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Asymptotic in a class of network models with an increasing sub-Gamma degree sequence

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Listed:
  • Jing Luo
  • Haoyu Wei
  • Xiaoyu Lei
  • Jiaxin Guo

Abstract

For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real data example are provided to illustrate asymptotic results.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2111.01301
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    References listed on IDEAS

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    1. Lu Pan & Ting Yan, 2020. "Asymptotics in the β-model for networks with a differentially private degree sequence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(18), pages 4378-4393, September.
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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.
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    6. 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.
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