IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v163y2020ics0167715220300821.html
   My bibliography  Save this article

A note on new Bernstein-type inequalities for the log-likelihood function of Bernoulli variables

Author

Listed:
  • Zhao, Yunpeng

Abstract

We prove a new Bernstein-type inequality for the log-likelihood function of Bernoulli variables. In contrast to classical Bernstein’s inequality and Hoeffding’s inequality when applied to this log-likelihood, the new bound is independent of the parameters of the Bernoulli variables and therefore does not blow up as the parameters approach 0 or 1. The new inequality strengthens certain theoretical results on likelihood-based methods for community detection in networks and can be applied to other likelihood-based methods for binary data.

Suggested Citation

  • Zhao, Yunpeng, 2020. "A note on new Bernstein-type inequalities for the log-likelihood function of Bernoulli variables," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220300821
    DOI: 10.1016/j.spl.2020.108779
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220300821
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108779?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. D. S. Choi & P. J. Wolfe & E. M. Airoldi, 2012. "Stochastic blockmodels with a growing number of classes," Biometrika, Biometrika Trust, vol. 99(2), pages 273-284.
    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. Fei Ma & Yixuan Wang & Kum Fai Yuen & Wenlin Wang & Xiaodan Li & Yuan Liang, 2019. "The Evolution of the Spatial Association Effect of Carbon Emissions in Transportation: A Social Network Perspective," IJERPH, MDPI, vol. 16(12), pages 1-23, June.
    2. Thibaut Lamadon & Elena Manresa & Stephane Bonhomme, 2016. "Discretizing Unobserved Heterogeneity," 2016 Meeting Papers 1536, Society for Economic Dynamics.
    3. Olga Klopp & Nicolas Verzelen, 2017. "Optimal graphon estimation in cut distance," Working Papers 2017-42, Center for Research in Economics and Statistics.
    4. Hric, Darko & Kaski, Kimmo & Kivelä, Mikko, 2018. "Stochastic block model reveals maps of citation patterns and their evolution in time," Journal of Informetrics, Elsevier, vol. 12(3), pages 757-783.
    5. Tin Lok James Ng & Thomas Brendan Murphy, 2021. "Weighted stochastic block model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1365-1398, December.
    6. Zhang, Yue & Yuan, Mingao, 2020. "Nonreconstruction of high-dimensional stochastic block model with bounded degree," Statistics & Probability Letters, Elsevier, vol. 158(C).
    7. Dragana M. Pavlović & Bryan R.L. Guillaume & Soroosh Afyouni & Thomas E. Nichols, 2020. "Multi‐subject stochastic blockmodels with mixed effects for adaptive analysis of individual differences in human brain network cluster structure," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 363-396, August.
    8. Yunpeng Zhao & Qing Pan & Chengan Du, 2019. "Logistic regression augmented community detection for network data with application in identifying autism‐related gene pathways," Biometrics, The International Biometric Society, vol. 75(1), pages 222-234, March.
    9. Lee, Kevin H. & Xue, Lingzhou & Hunter, David R., 2020. "Model-based clustering of time-evolving networks through temporal exponential-family random graph models," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    10. Babkin, Sergii & Stewart, Jonathan R. & Long, Xiaochen & Schweinberger, Michael, 2020. "Large-scale estimation of random graph models with local dependence," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    11. Tian, Yahui & Gel, Yulia R., 2019. "Fusing data depth with complex networks: Community detection with prior information," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 99-116.
    12. Haiyan Liu & Ick Hoon Jin & Zhiyong Zhang & Ying Yuan, 2021. "Social Network Mediation Analysis: A Latent Space Approach," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 272-298, March.
    13. Sirio Legramanti & Tommaso Rigon & Daniele Durante, 2022. "Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 108-126, June.

    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:eee:stapro:v:163:y:2020:i:c:s0167715220300821. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.