IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i3d10.1007_s00362-019-01127-6.html
   My bibliography  Save this article

Flexible sliced Latin hypercube designs with slices of different sizes

Author

Listed:
  • Ru Yuan

    (Zhongnan University of Economics and Law
    Nankai University)

  • Bing Guo

    (Sichuan University
    Nankai University)

  • Min-Qian Liu

    (Nankai University)

Abstract

Sliced Latin hypercube designs (SLHDs) are widely used in various computer experiments. Literatures concerning the construction of SLHDs are all about constructing SLHDs with slices of the same size. However, in some cases, e.g. when an experiment with multiple computer models having different complexities or a sequential experiment with varying costs in different periods is considered, SLHDs with slices of different sizes are preferable. In this paper, we propose a new class of SLHD, named the flexible SLHD, in which the whole design is a Latin hypercube design (LHD), and each slice is also an LHD when its levels being properly collapsed, the difference lies in that its slices may have different run sizes. Several methods for constructing such designs are developed. Theoretical results on the constructed designs are derived, and discussion on the slice sizes of the constructed flexible SLHDs is provided. Furthermore, an optimization algorithm is developed to improve the space-filling property of the constructed SLHDs. The newly proposed flexible SLHD is also a special nested LHD (Qian in Biometrika 96:957–970, 2009), each of its slice can be viewed as a small LHD nested in the whole design.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01127-6
    DOI: 10.1007/s00362-019-01127-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-019-01127-6
    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/s00362-019-01127-6?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. Peter Z. G. Qian, 2012. "Sliced Latin Hypercube Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 393-399, March.
    3. Peter Z. G. Qian, 2009. "Nested Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 957-970.
    4. Xiangshun Kong & Mingyao Ai & Kwok Leung Tsui, 2018. "Flexible sliced designs for computer experiments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 631-646, June.
    5. 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.
    6. David M. Steinberg & Dennis K. J. Lin, 2006. "A construction method for orthogonal Latin hypercube designs," Biometrika, Biometrika Trust, vol. 93(2), pages 279-288, June.
    7. 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.
    8. Derek Bingham & Randy R. Sitter & Boxin Tang, 2009. "Orthogonal and nearly orthogonal designs for computer experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 51-65.
    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. 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.

    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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Weiping Zhou & Jinyu Yang & Min-Qian Liu, 2021. "Construction of orthogonal marginally coupled designs," Statistical Papers, Springer, vol. 62(4), pages 1795-1820, August.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Li, Hui & Yang, Liuqing & Liu, Min-Qian, 2022. "Construction of space-filling orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 180(C).
    15. Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    16. 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.
    17. 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.
    18. Jing Zhang & Jin Xu & Kai Jia & Yimin Yin & Zhengming Wang, 2019. "Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes," Mathematics, MDPI, vol. 7(9), pages 1-16, September.
    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. 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.

    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:62:y:2021:i:3:d:10.1007_s00362-019-01127-6. 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.