IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v119y2016icp226-234.html
   My bibliography  Save this article

Spherical discrepancy for designs on hyperspheres

Author

Listed:
  • Zhang, Mei
  • Zhou, Yong-Dao

Abstract

The discrepancies have played an important role in quasi-Monte Carlo Methods. There are various discrepancies for measuring the uniformity of a set of points on unit hypercube and simplex. However, there is no discrepancy with explicit expressions on hyperspheres in the literature. In this paper, we propose a new measure of uniformity, called spherical discrepancy (SD), for designs on the unit hypersphere. Different with the pseudo F-discrepancy, the SD is directly defined on the unit hypersphere in terms of spherical coordinates. A computational formula of the new discrepancy is also given by the functional method. The properties of SD and some illustrative examples are also shown.

Suggested Citation

  • Zhang, Mei & Zhou, Yong-Dao, 2016. "Spherical discrepancy for designs on hyperspheres," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 226-234.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:226-234
    DOI: 10.1016/j.spl.2016.08.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715216301547
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.08.009?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. Chuang, S.C. & Hung, Y.C., 2010. "Uniform design over general input domains with applications to target region estimation in computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 219-232, January.
    2. David H. Doehlert, 1970. "Uniform Shell Designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 19(3), pages 231-239, November.
    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. Xiong, Zikang & Liu, Liwei & Ning, Jianhui & Qin, Hong, 2020. "Sphere packing design for experiments with mixtures," Statistics & Probability Letters, Elsevier, vol. 164(C).
    2. Chen, Ray-Bing & Hsu, Yen-Wen & Hung, Ying & Wang, Weichung, 2014. "Discrete particle swarm optimization for constructing uniform design on irregular regions," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 282-297.
    3. Lin, D.K.J. & Sharpe, C. & Winker, P., 2010. "Optimized U-type designs on flexible regions," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1505-1515, June.
    4. Román-Ramírez, L.A. & Marco, J., 2022. "Design of experiments applied to lithium-ion batteries: A literature review," Applied Energy, Elsevier, vol. 320(C).
    5. Astrid Jourdan, 2024. "Space-filling designs with a Dirichlet distribution for mixture experiments," Statistical Papers, Springer, vol. 65(5), pages 2667-2686, July.
    6. Ray-Bing Chen & Ying-Chao Hung & Weichung Wang & Sung-Wei Yen, 2013. "Contour estimation via two fidelity computer simulators under limited resources," Computational Statistics, Springer, vol. 28(4), pages 1813-1834, August.
    7. Fockink, Douglas H. & Morais, Ana R.C. & Ramos, Luiz P. & Łukasik, Rafał M., 2018. "Insight into the high-pressure CO2 pre-treatment of sugarcane bagasse for a delivery of upgradable sugars," Energy, Elsevier, vol. 151(C), pages 536-544.

    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:119:y:2016:i:c:p:226-234. 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.