IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v210y2025ics0047259x25000570.html

Understanding asymptotic consistency and its unique advantages in large sample statistical inference

Author

Listed:
  • Wang, Jiangzhou
  • Liu, Binghui
  • Jing, Bing-Yi
  • Guo, Jianhua

Abstract

The main objective of this paper is to investigate the usefulness of asymptotic consistency in large-sample statistical inference. In many statistical applications, plug-in methods are used to construct statistics, which raises the natural question of whether the asymptotic properties of Tn(βˆn,αˆn) remain unchanged when the estimator αˆn is replaced by its corresponding target quantity αn. We establish that if αˆn is asymptotically consistent for αn, meaning that limn→∞P(αˆn=αn)=1, then Tn(βˆn,αˆn) and Tn(βˆn,αn) share identical asymptotic behaviors in terms of convergence and limiting distribution. This result notably simplifies the derivation of asymptotic properties, especially when the dependency between βˆn and αˆn is complex. Furthermore, we systematically explore the relationship between asymptotic consistency and traditional forms of consistency, such as weak and strong consistency, clarifying their distinctions through theorems and counterexamples. Finally, the theoretical findings are demonstrated via three specific applications, illustrating the practical benefits of asymptotic consistency in large-sample inference.

Suggested Citation

  • Wang, Jiangzhou & Liu, Binghui & Jing, Bing-Yi & Guo, Jianhua, 2025. "Understanding asymptotic consistency and its unique advantages in large sample statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:jmvana:v:210:y:2025:i:c:s0047259x25000570
    DOI: 10.1016/j.jmva.2025.105462
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X25000570
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2025.105462?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Jianwei Hu & Jingfei Zhang & Hong Qin & Ting Yan & Ji Zhu, 2021. "Using Maximum Entry-Wise Deviation to Test the Goodness of Fit for Stochastic Block Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1373-1382, 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. Wu, Qianyong & Hu, Jiang, 2024. "Two-sample test of stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    2. Fei Ye & Jingsong Xiao & Weidong Ma & Shiwen Jin & Ying Yang, 2025. "Detecting small clusters in the stochastic block model," Statistical Papers, Springer, vol. 66(2), pages 1-34, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:jmvana:v:210:y:2025:i:c:s0047259x25000570. 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.