IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i3d10.1007_s00362-022-01347-3.html
   My bibliography  Save this article

Construction of orthogonal general sliced Latin hypercube designs

Author

Listed:
  • Bing Guo

    (Sichuan University)

  • Xiao-Rong Li

    (LPMC & KLMDASR, Nankai University)

  • Min-Qian Liu

    (LPMC & KLMDASR, Nankai University)

  • Xue Yang

    (School of Statistics, Tianjin University of Finance and Economics)

Abstract

Computer experiments have attracted increasing attention in recent decades. General sliced Latin hypercube design (LHD), which is a sliced LHD with multiple layers and at each layer of which each slice can be further divided into smaller LHDs at the above layer, is widely applied in computer experiments with qualitative and quantitative factors, multiple model experiments, cross-validation, and stochastic optimization. Orthogonality is an important property for LHDs. Methods for constructing orthogonal and nearly orthogonal general sliced LHDs are put forward first time in this paper, where orthogonal designs and structural vectors are used in the constructions. The resulting designs not only possess orthogonality in the whole designs, but also achieve orthogonality in each layer before and after being collapsed. Furthermore, based on different structural vectors, the methods can be easily extended to construct orthogonal LHDs with some desired sliced or nested structures.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:3:d:10.1007_s00362-022-01347-3
    DOI: 10.1007/s00362-022-01347-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01347-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-022-01347-3?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. Wang, Xiao-Lei & Zhao, Yu-Na & Yang, Jian-Feng & Liu, Min-Qian, 2017. "Construction of (nearly) orthogonal sliced Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 174-180.
    2. Vikram V. Garg & Roy H. Stogner, 2017. "Hierarchical Latin Hypercube Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 673-682, April.
    3. Bing Guo & Xue-Ping Chen & Min-Qian Liu, 2020. "Construction of Latin hypercube designs with nested and sliced structures," Statistical Papers, Springer, vol. 61(2), pages 727-740, April.
    4. Fasheng Sun & Min-Qian Liu & Dennis K. J. Lin, 2009. "Construction of orthogonal Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 971-974.
    5. Yaping Wang & Fasheng Sun & Hongquan Xu, 2022. "On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 375-385, January.
    6. Fasheng Sun & Boxin Tang, 2017. "A general rotation method for orthogonal Latin hypercubes," Biometrika, Biometrika Trust, vol. 104(2), pages 465-472.
    7. 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.
    8. 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.
    9. Yaping Wang & Jianfeng Yang & Hongquan Xu, 2018. "On the connection between maximin distance designs and orthogonal designs," Biometrika, Biometrika Trust, vol. 105(2), pages 471-477.
    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. Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    2. 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.
    3. 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.
    4. Li, Hui & Yang, Liuqing & Liu, Min-Qian, 2022. "Construction of space-filling orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 180(C).
    5. 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.
    6. Weiping Zhou & Jinyu Yang & Min-Qian Liu, 2021. "Construction of orthogonal marginally coupled designs," Statistical Papers, Springer, vol. 62(4), pages 1795-1820, August.
    7. 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.
    8. 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.
    9. Weiyan Mu & Chengxin Liu & Shifeng Xiong, 2023. "Nested Maximum Entropy Designs for Computer Experiments," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    10. 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.
    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. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Li Gu & Jian-Feng Yang, 2013. "Construction of nearly orthogonal Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 819-830, August.
    19. 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.
    20. Wang, Xiaodi & Huang, Hengzhen, 2023. "Group symmetric Latin hypercube designs for symmetrical global sensitivity analysis," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

    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:stpapr:v:64:y:2023:i:3:d:10.1007_s00362-022-01347-3. 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.