IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v129y2017icp269-274.html
   My bibliography  Save this article

Upper bound on the number of multi-level columns in equally replicated optimal designs minimizing the E(fNOD) criterion

Author

Listed:
  • Chasiotis, Vasilis
  • Kounias, Stratis
  • Farmakis, Nikolaos

Abstract

This article provides an upper bound on the number of multi-level columns, denoted by M, in equally replicated optimal designs, minimizing the E(fNOD) criterion. These designs are called E(fNOD)-optimal. Applying an algorithm and by row juxtaposition, fourteen E(fNOD)-optimal designs are constructed.

Suggested Citation

  • Chasiotis, Vasilis & Kounias, Stratis & Farmakis, Nikolaos, 2017. "Upper bound on the number of multi-level columns in equally replicated optimal designs minimizing the E(fNOD) criterion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 269-274.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:269-274
    DOI: 10.1016/j.spl.2017.06.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715217302122
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2017.06.008?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. Yamada, Shu & Lin, Dennis K. J., 1999. "Three-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 31-39, October.
    2. Kai-Tai Fang & Dennis K. J. Lin & Min-Qian Liu, 2003. "Optimal mixed-level supersaturated design," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 279-291, December.
    3. Mandal, B.N. & Koukouvinos, C., 2014. "Optimal multi-level supersaturated designs through integer programming," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 183-191.
    4. S. Georgiou & C. Koukouvinos, 2006. "Multi-level k-circulant Supersaturated Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 209-220, October.
    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. Mandal, B.N. & Koukouvinos, C., 2014. "Optimal multi-level supersaturated designs through integer programming," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 183-191.
    2. Chen, Jie & Liu, Min-Qian, 2008. "Optimal mixed-level supersaturated design with general number of runs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2496-2502, October.
    3. Armando Javier Ríos-Lira & Yaquelin Verenice Pantoja-Pacheco & José Antonio Vázquez-López & José Alfredo Jiménez-García & Martha Laura Asato-España & Moisés Tapia-Esquivias, 2021. "Alias Structures and Sequential Experimentation for Mixed-Level Designs," Mathematics, MDPI, vol. 9(23), pages 1-21, November.
    4. Li, Peng-Fei & Liu, Min-Qian & Zhang, Run-Chu, 2004. "Some theory and the construction of mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 105-116, August.
    5. Li, Hongyi & Qin, Hong, 2018. "Some new results on Triple designs," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 1-9.
    6. Gupta, V.K. & Singh, Poonam & Kole, Basudev & Parsad, Rajender, 2009. "Construction of efficient unbalanced mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2359-2366, November.
    7. Koukouvinos, C. & Stylianou, S., 2004. "Optimal multi-level supersaturated designs constructed from linear and quadratic functions," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 199-211, August.
    8. Koukouvinos, C. & Mantas, P., 2005. "Construction of some E(fNOD) optimal mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 312-321, October.
    9. Liu, Min-Qian & Zhang, Li, 2009. "An algorithm for constructing mixed-level k-circulant supersaturated designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2465-2470, May.
    10. Yan Liu & Min-Qian Liu, 2012. "Construction of equidistant and weak equidistant supersaturated designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 33-53, January.
    11. K. Chatterjee & K. Drosou & S. D. Georgiou & C. Koukouvinos, 2018. "Multi-level and mixed-level k-circulant supersaturated designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 337-355, April.
    12. Bochuan Jiang & Yaping Wang & Mingyao Ai, 2022. "Search for minimum aberration designs with uniformity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 271-287, April.
    13. Nguyen, Nam-Ky & Liu, Min-Qian, 2008. "An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5269-5276, August.
    14. Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing, 2008. "Lee discrepancy and its applications in experimental designs," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1933-1942, September.
    15. Rong-Xian Yue & Kashinath Chatterjee, 2010. "Bayesian U-type design for nonparametric response surface prediction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 219-231, September.
    16. S. Georgiou & C. Koukouvinos, 2006. "Multi-level k-circulant Supersaturated Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 209-220, October.
    17. Narayanaswamy Balakrishnan & Hong Qin & Kashinath Chatterjee, 2016. "Generalized projection discrepancy and its applications in experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 19-35, January.
    18. Sarkar, Angshuman & Lin, Dennis K.J. & Chatterjee, Kashinath, 2009. "Probability of correct model identification in supersaturated design," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1224-1230, May.
    19. Gao, Yanping & Yi, Siyu & Zhou, Yongdao, 2022. "Maximin L1-distance Range-fixed Level-augmented designs," Statistics & Probability Letters, Elsevier, vol. 186(C).
    20. Yamada, Shu & Matsui, Michiyo & Matsui, Tomomi & Lin, Dennis K.J. & Takahashi, Takenori, 2006. "A general construction method for mixed-level supersaturated design," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 254-265, January.

    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:129:y:2017:i:c:p:269-274. 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.