IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v26y2023i1d10.1007_s11203-022-09273-9.html
   My bibliography  Save this article

A functional central limit theorem on non-stationary random fields with nested spatial structure

Author

Listed:
  • Leshun Xu

    (University of Auckland
    Simon Fraser University)

  • Alan Lee

    (University of Auckland)

  • Thomas Lumley

    (University of Auckland)

Abstract

In this paper, we establish a functional central limit theorem on high dimensional random fields in the context of model-based survey analysis. For strongly-mixing non-stationary random fields, we provide an upper bound for the fourth moment of the finite population total. This inequality is the generalization of a key tool for proving functional central limit theorems in Rio (Asymptotic theory of weakly dependent random processes, Springer, Berlin, 2017). Under the nested sampling strategy, we introduce assumptions on strongly-mixing coefficients and quantile functions to show that a functional stochastic process asymptotically approaches to a Gaussian process.

Suggested Citation

  • Leshun Xu & Alan Lee & Thomas Lumley, 2023. "A functional central limit theorem on non-stationary random fields with nested spatial structure," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 215-234, April.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:1:d:10.1007_s11203-022-09273-9
    DOI: 10.1007/s11203-022-09273-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11203-022-09273-9
    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/s11203-022-09273-9?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. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    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. Dagmara Dudek & Anna Kuczmaszewska, 2024. "Some practical and theoretical issues related to the quantile estimators," Statistical Papers, Springer, vol. 65(6), pages 3917-3933, August.
    2. Richard C. Bradley & Cristina Tone, 2017. "A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields," Journal of Theoretical Probability, Springer, vol. 30(2), pages 655-674, June.
    3. Bernou, Ismahen & Boukhari, Fakhreddine, 2022. "Limit theorems for dependent random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 189(C).
    4. Li, Kunpeng, 2022. "Threshold spatial autoregressive model," MPRA Paper 113568, University Library of Munich, Germany.
    5. Thành, Lê Vǎn, 2024. "On Rio’s proof of limit theorems for dependent random fields," Stochastic Processes and their Applications, Elsevier, vol. 171(C).

    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:sistpr:v:26:y:2023:i:1:d:10.1007_s11203-022-09273-9. 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.