IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v12y1999i2d10.1023_a1021626127372.html
   My bibliography  Save this article

A Cramér Type Large Deviation Result for Student's t-Statistic

Author

Listed:
  • Qi-Man Shao

    (University of Oregon)

Abstract

Let X, X 1, X 2,... be independent and identically distributed random variables with a finite third moment, and let T n be the Student's t-statistic. This paper shows that lim n→∞ P(T n>x)/P(t n>x)=1 holds uniformly in 0≤x≤o(n 1/6), where t n has a t-distribution with n−1 degrees of freedom. An example is also given to show that a finite third moment is necessary for this result.

Suggested Citation

  • Qi-Man Shao, 1999. "A Cramér Type Large Deviation Result for Student's t-Statistic," Journal of Theoretical Probability, Springer, vol. 12(2), pages 385-398, April.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:2:d:10.1023_a:1021626127372
    DOI: 10.1023/A:1021626127372
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021626127372
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1021626127372?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. Xuming He & Qi-man Shao, 1996. "Bahadur efficiency and robustness of studentized score tests," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 295-314, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xinwei Feng & Qi-Man Shao & Ofer Zeitouni, 2021. "Self-normalized Moderate Deviations for Random Walk in Random Scenery," Journal of Theoretical Probability, Springer, vol. 34(1), pages 103-124, March.
    2. Bing-Yi Jing & Qiying Wang & Wang Zhou, 2015. "Cramér-Type Moderate Deviation for Studentized Compound Poisson Sum," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1556-1570, December.
    3. Qiying Wang, 2011. "Refined Self-normalized Large Deviations for Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 24(2), pages 307-329, June.
    4. Han-Ying Liang & Josef G. Steinebach, 2006. "Self-Normalized LIL for Hanson–Russo Type Increments," Journal of Theoretical Probability, Springer, vol. 19(1), pages 70-88, January.

    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. Masahiro Kato, 2023. "Locally Optimal Fixed-Budget Best Arm Identification in Two-Armed Gaussian Bandits with Unknown Variances," Papers 2312.12741, arXiv.org, revised Mar 2024.

    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:jotpro:v:12:y:1999:i:2:d:10.1023_a:1021626127372. 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.