IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v63y2022i2d10.1007_s00362-021-01243-2.html
   My bibliography  Save this article

Affiliation weighted networks with a differentially private degree sequence

Author

Listed:
  • Jing Luo

    (South Central University for Nationalities)

  • Tour Liu

    (Tianjin Normal University)

  • Qiuping Wang

    (Central China Normal University)

Abstract

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. The asymptotic theorem of a differentially private estimator of the parameter in the private $$p_{0}$$ p 0 model has been established. However, the $$p_{0}$$ p 0 model only focuses on binary edges for one-mode network. In many case, the connections in many affiliation networks (two-mode) could be weighted, taking a set of finite discrete values. In this paper, we derive the consistency and asymptotic normality of the moment estimators of parameters in affiliation finite discrete weighted networks with a differentially private degree sequence. Simulation studies and a real data example demonstrate our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01243-2
    DOI: 10.1007/s00362-021-01243-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-021-01243-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-021-01243-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Su, Liju & Qian, Xiaodi & Yan, Ting, 2018. "A note on a network model with degree heterogeneity and homophily," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 27-30.
    2. Xiaofang He & Wangxue Chen & Wenshu Qian, 2020. "Maximum likelihood estimators of the parameters of the log-logistic distribution," Statistical Papers, Springer, vol. 61(5), pages 1875-1892, October.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Yong Zhang & Xiaodi Qian & Hong Qin & Ting Yan, 2017. "Affiliation networks with an increasing degree sequence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(22), pages 11163-11180, November.
    8. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Mingli Chen & Kengo Kato & Chenlei Leng, 2021. "Analysis of networks via the sparse β‐model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 887-910, November.
    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. Ma, Shujie & Su, Liangjun & Zhang, Yichong, 2020. "Detecting Latent Communities in Network Formation Models," Economics and Statistics Working Papers 12-2020, Singapore Management University, School of Economics.
    5. Gao, Wayne Yuan & Li, Ming & Xu, Sheng, 2023. "Logical differencing in dyadic network formation models with nontransferable utilities," Journal of Econometrics, Elsevier, vol. 235(1), pages 302-324.
    6. Han, Ruijian & Chen, Kani & Tan, Chunxi, 2020. "Bivariate gamma model," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    7. Zhao, Yunpeng, 2022. "Network inference from temporally dependent grouped observations," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    8. 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.
    9. 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.
    10. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    11. David W. Hughes, 2021. "Estimating Nonlinear Network Data Models with Fixed Effects," Boston College Working Papers in Economics 1058, Boston College Department of Economics.
    12. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.
    13. Koen Jochmans & Martin Weidner, 2019. "Fixed‐Effect Regressions on Network Data," Econometrica, Econometric Society, vol. 87(5), pages 1543-1560, September.
    14. Andreas Dzemski, 2019. "An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 763-776, December.
    15. Bartolucci, Francesco & Pigini, Claudia & Valentini, Francesco, 2021. "MCMC Conditional Maximum Likelihood for the two-way fixed-effects logit," MPRA Paper 110034, University Library of Munich, Germany.
    16. Junhui Cai & Dan Yang & Wu Zhu & Haipeng Shen & Linda Zhao, 2021. "Network regression and supervised centrality estimation," Papers 2111.12921, arXiv.org.
    17. Junlong Zhao & Xiumin Liu & Hansheng Wang & Chenlei Leng, 2022. "Dimension reduction for covariates in network data [On semidefinite relaxations for the block model]," Biometrika, Biometrika Trust, vol. 109(1), pages 85-102.
    18. Su, Liju & Qian, Xiaodi & Yan, Ting, 2018. "A note on a network model with degree heterogeneity and homophily," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 27-30.
    19. Tadao Hoshino, 2020. "A Pairwise Strategic Network Formation Model with Group Heterogeneity: With an Application to International Travel," Papers 2012.14886, arXiv.org, revised Feb 2021.
    20. Luis E. Candelaria, 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," Papers 2007.05403, arXiv.org, revised Aug 2020.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01243-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.