IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v156y2020ics016771521930269x.html
   My bibliography  Save this article

A hypothesis-testing perspective on the G-normal distribution theory

Author

Listed:
  • Peng, Shige
  • Zhou, Quan

Abstract

The G-normal distribution was introduced by Peng (2007) as the limiting distribution in the central limit theorem for sublinear expectation spaces. Equivalently, it can be interpreted as the solution to a stochastic control problem where we have a sequence of random variables, whose variances can be chosen based on all past information. In this note we study the tail behavior of the G-normal distribution through analyzing a nonlinear heat equation. Asymptotic results are provided so that the tail “probabilities” can be easily evaluated with high accuracy. This study also has a significant impact on the hypothesis testing theory for heteroscedastic data; we show that even if the data are generated under the null hypothesis, it is possible to cheat and attain statistical significance by sequentially manipulating the error variances of the observations.

Suggested Citation

  • Peng, Shige & Zhou, Quan, 2020. "A hypothesis-testing perspective on the G-normal distribution theory," Statistics & Probability Letters, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:stapro:v:156:y:2020:i:c:s016771521930269x
    DOI: 10.1016/j.spl.2019.108623
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521930269X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.108623?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.

    Citations

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


    Cited by:

    1. Xuekang Zhang & Shounian Deng & Weiyin Fei, 2023. "Nonparametric Estimation of Trend for Stochastic Processes Driven by G-Brownian Motion with Small Noise," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-14, June.
    2. Shige Peng & Huilin Zhang, 2022. "Wong–Zakai Approximation for Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(1), pages 410-425, March.

    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:156:y:2020:i:c:s016771521930269x. 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/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.