IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v96y2009i1p243-247.html
   My bibliography  Save this article

Construction of orthogonal and nearly orthogonal Latin hypercubes

Author

Listed:
  • C. Devon Lin
  • Rahul Mukerjee
  • Boxin Tang

Abstract

We propose a method for constructing orthogonal or nearly orthogonal Latin hypercubes. The method yields a large Latin hypercube by coupling an orthogonal array of index unity with a small Latin hypercube. It is shown that the large Latin hypercube inherits the exact or near orthogonality of the small Latin hypercube. Thus, effort for searching for large Latin hypercubes, that are exactly or nearly orthogonal, can be focussed on finding small Latin hypercubes with the same property. We obtain a useful collection of orthogonal or nearly orthogonal Latin hypercubes, which have a large factor-to-run ratio and the results are often much more economical than existing methods. Copyright 2009, Oxford University Press.

Suggested Citation

  • C. Devon Lin & Rahul Mukerjee & Boxin Tang, 2009. "Construction of orthogonal and nearly orthogonal Latin hypercubes," Biometrika, Biometrika Trust, vol. 96(1), pages 243-247.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:243-247
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asn064
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Song-Nan Liu & Min-Qian Liu & Jin-Yu Yang, 2023. "Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    2. Bing Guo & Xiao-Rong Li & Min-Qian Liu & Xue Yang, 2023. "Construction of orthogonal general sliced Latin hypercube designs," Statistical Papers, Springer, vol. 64(3), pages 987-1014, June.
    3. Stelios Georgiou & Christos Koukouvinos & Min-Qian Liu, 2014. "U-type and column-orthogonal designs for computer experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 1057-1073, November.
    4. Qing Liu & Neeraj Arora, 2011. "Efficient Choice Designs for a Consider-Then-Choose Model," Marketing Science, INFORMS, vol. 30(2), pages 321-338, 03-04.
    5. Wang, Sumin & Wang, Dongying & Sun, Fasheng, 2019. "A central limit theorem for marginally coupled designs," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 168-174.
    6. Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    7. Mandal, B.N. & Dash, Sukanta & Parui, Shyamsundar & Parsad, Rajender, 2016. "Orthogonal Latin hypercube designs with special reference to four factors," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 181-185.
    8. Fasheng Sun & Boxin Tang, 2017. "A Method of Constructing Space-Filling Orthogonal Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 683-689, April.
    9. Wenlong Li & Min-Qian Liu & Jian-Feng Yang, 2022. "Construction of column-orthogonal strong orthogonal arrays," Statistical Papers, Springer, vol. 63(2), pages 515-530, April.
    10. Ru Yuan & Bing Guo & Min-Qian Liu, 2021. "Flexible sliced Latin hypercube designs with slices of different sizes," Statistical Papers, Springer, vol. 62(3), pages 1117-1134, June.
    11. Zong-Feng Qi & Xue-Ru Zhang & Yong-Dao Zhou, 2018. "Generalized good lattice point sets," Computational Statistics, Springer, vol. 33(2), pages 887-901, June.
    12. Sigal Levy & David Steinberg, 2010. "Computer experiments: a review," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(4), pages 311-324, December.
    13. Chen, Hao & Yang, Jinyu & Lin, Dennis K.J. & Liu, Min-Qian, 2019. "Sliced Latin hypercube designs with both branching and nested factors," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 124-131.
    14. Weiping Zhou & Jinyu Yang & Min-Qian Liu, 2021. "Construction of orthogonal marginally coupled designs," Statistical Papers, Springer, vol. 62(4), pages 1795-1820, August.
    15. Ifigenia Efthimiou & Stelios Georgiou & Min-Qian Liu, 2015. "Construction of nearly orthogonal Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 45-57, January.
    16. Li, Hui & Yang, Liuqing & Liu, Min-Qian, 2022. "Construction of space-filling orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 180(C).
    17. Sukanta Dash & Baidya Nath Mandal & Rajender Parsad, 2020. "On the construction of nested orthogonal Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 347-353, April.
    18. Tonghui Pang & Yan Wang & Jian-Feng Yang, 2022. "Asymptotically optimal maximin distance Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 405-418, May.

    More about this item

    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:oup:biomet:v:96:y:2009:i:1:p:243-247. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.