IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v251y2025ics0304407625001083.html
   My bibliography  Save this article

Bernstein-type inequalities and nonparametric estimation under near-epoch dependence

Author

Listed:
  • Yuan, Zihao
  • Spindler, Martin

Abstract

The main contributions of this paper are twofold. First, we derive Bernstein-type inequalities for irregularly spaced data under near-epoch dependent (NED) conditions and deterministic domain-expanding-infill (DEI) asymptotics. By introducing the concept of “effective dimension” to describe the geometric structure of sampled locations, we illustrate – unlike previous research – that the sharpness of these inequalities is affected by this effective dimension. To our knowledge, ours is the first study to report this phenomenon and show Bernstein-type inequalities under deterministic DEI asymptotics. This work represents a direct generalization of the work of Xu and Lee (2018), thus marking an important contribution to the topic. As a corollary, we derive a Bernstein-type inequality for irregularly spaced α-mixing random fields under DEI asymptotics. Our second contribution is to apply these inequalities to explore the attainability of optimal convergence rates for the local linear conditional mean estimator under algebraic NED conditions. Our results illustrate how the effective dimension affects assumptions of dependence. This finding refines the results of Jenish (2012) and extends the work of Hansen (2008), Vogt (2012), Chen and Christensen (2015) and Li, Lu, and Linton (2012).

Suggested Citation

  • Yuan, Zihao & Spindler, Martin, 2025. "Bernstein-type inequalities and nonparametric estimation under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 251(C).
    • Handle: RePEc:eee:econom:v:251:y:2025:i:c:s0304407625001083
    DOI: 10.1016/j.jeconom.2025.106054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407625001083
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2025.106054?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.

    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:econom:v:251:y:2025:i:c:s0304407625001083. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/locate/jeconom .

    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.