IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v164y2021ics0167947321001390.html
   My bibliography  Save this article

On efficient exact experimental designs for ordered treatments

Author

Listed:
  • Singh, Satya Prakash
  • Davidov, Ori

Abstract

In a recent paper Singh and Davidov (2019) derive approximate optimal designs for experiments with ordered treatments. Specifically, maxi–min and intersection–union designs were explored. These designs, which address different types of hypothesis testing problems, provide a substantial improvement over standard designs in terms of power, or equivalently, sample size requirements. In practice however, exact, not approximate designs are used. Therefore, in this paper, we develop methods for finding efficient exact designs for the testing problems considered in Singh and Davidov (2019). The proposed designs are compared numerically to some well known existing designs and it is shown that the new designs require fewer experimental units to attain prespecified power. A thorough sensitivity analysis shows that the proposed designs are robust against possible misspecification of the parameters under the alternative and the order relation among the treatment groups.

Suggested Citation

  • Singh, Satya Prakash & Davidov, Ori, 2021. "On efficient exact experimental designs for ordered treatments," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:csdana:v:164:y:2021:i:c:s0167947321001390
    DOI: 10.1016/j.csda.2021.107305
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947321001390
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2021.107305?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. Satya Prakash Singh & Ori Davidov, 2019. "On the design of experiments with ordered treatments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(5), pages 881-900, November.
    2. Shyamal D. Peddada & Joseph K. Haseman & Xiaofeng Tan & Greg Travlos, 2006. "Tests for a simple tree order restriction with application to dose–response studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(4), pages 493-506, August.
    3. L. Imhof & J. Lopez‐Fidalgo & W. K. Wong, 2001. "Efficiencies of Rounded Optimal Approximate Designs for Small Samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 301-318, November.
    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. Belmiro P. M. Duarte & Anthony C. Atkinson & Satya P. Singh & Marco S. Reis, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," Statistical Papers, Springer, vol. 64(2), pages 587-615, April.
    2. Duarte, Belmiro P.M. & Atkinson, Anthony C. & P. Singh, Satya & S. Reis, Marco, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," LSE Research Online Documents on Economics 115187, London School of Economics and Political Science, LSE Library.

    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. Belmiro P. M. Duarte, 2023. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    2. Kulan Ranasinghe & Mervyn J. Silvapulle, 2008. "Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown," Monash Econometrics and Business Statistics Working Papers 5/08, Monash University, Department of Econometrics and Business Statistics.
    3. Duarte, Belmiro P.M. & Atkinson, Anthony C. & P. Singh, Satya & S. Reis, Marco, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," LSE Research Online Documents on Economics 115187, London School of Economics and Political Science, LSE Library.
    4. Víctor Casero-Alonso & Jesús López-Fidalgo, 2015. "Optimal designs subject to cost constraints in simultaneous equations models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 701-713, December.
    5. Àngela Sebastià Bargues & José-Luis Polo Sanz & Raúl Martín Martín, 2022. "Optimal Experimental Design for Parametric Identification of the Electrical Behaviour of Bioelectrodes and Biological Tissues," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    6. Kulan Ranasinghe & Mervyn J. Silvapulle, 2008. "Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown," Monash Econometrics and Business Statistics Working Papers 1/08, Monash University, Department of Econometrics and Business Statistics.
    7. Eryl Shirley, 2007. "Tests for a simple tree order restriction with application to dose–response studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 493-494, August.
    8. Belmiro P. M. Duarte & Anthony C. Atkinson & Satya P. Singh & Marco S. Reis, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," Statistical Papers, Springer, vol. 64(2), pages 587-615, April.
    9. Harman, Radoslav & Filová, Lenka, 2014. "Computing efficient exact designs of experiments using integer quadratic programming," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1159-1167.

    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:csdana:v:164:y:2021:i:c:s0167947321001390. 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/locate/csda .

    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.