IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v56y2015i1p105-119.html
   My bibliography  Save this article

Optimum mixture designs in a restricted region

Author

Listed:
  • Nripes Mandal
  • Manisha Pal
  • Bikas Sinha
  • Premadhis Das

Abstract

In a mixture experiment, the response depends on the proportions of the mixing components. Canonical models of different degrees and also other models have been suggested to represent the mean response. Optimum designs for estimation of the parameters of the models have been investigated by different authors. In most cases, the optimum design includes the vertex points of the simplex as support points of the design, which are not mixture combinations in the true non-trivial sense. In this paper, optimum designs have been obtained when the experimental region is an ellipsoidal subspace of the entire factor space which does not cover the vertex points of the simplex. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Nripes Mandal & Manisha Pal & Bikas Sinha & Premadhis Das, 2015. "Optimum mixture designs in a restricted region," Statistical Papers, Springer, vol. 56(1), pages 105-119, February.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:1:p:105-119
    DOI: 10.1007/s00362-013-0568-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-013-0568-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-013-0568-0?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. Shuangzhe Liu & Heinz Neudecker, 1997. "Experiments with mixtures: Optimal allocations for becker’s models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 53-66, January.
    2. Kim-Hung Li & Tai-Shing Lau & Chongqi Zhang, 2005. "A note on D-optimal designs for models with and without an intercept," Statistical Papers, Springer, vol. 46(3), pages 451-458, July.
    3. Manisha Pal & Nripes Mandal, 2009. "Optimum designs for estimation of optimum point under cost constraint," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(9), pages 999-1008.
    4. Pal, Manisha & Mandal, Nripes K., 2006. "Optimum designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1369-1379, July.
    5. Pal, Manisha & Mandal, Nripes Kumar, 2008. "Minimax designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 608-615, April.
    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. Haosheng Jiang & Chongqi Zhang, 2022. "Construction of Full Order-of-Addition Generalization Simplex-Centroid Designs by the Directed Graph Approach," Mathematics, MDPI, vol. 10(3), pages 1-13, January.

    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, N.K. & Pal, Manisha & Aggarwal, M.L., 2012. "Pseudo-Bayesian A-optimal designs for estimating the point of maximum in component-amount Darroch–Waller mixture model," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1088-1094.
    2. Mandal, Nripes Kumar & Pal, Manisha, 2013. "Maximin designs for the detection of synergistic effects," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1632-1637.
    3. Haoyu Wang & Chongqi Zhang, 2022. "The mixture design threshold accepting algorithm for generating $$\varvec{D}$$ D -optimal designs of the mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 345-371, April.
    4. Hilgers, Ralf-Dieter, 2000. "D-optimal design for Becker's minimum polynomial," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 175-179, August.
    5. Pal, Manisha & Mandal, Nripes Kumar, 2008. "Minimax designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 608-615, April.
    6. GOOS, Peter & JONES, Bradley & SYAFITRI, Utami, 2013. "I-optimal mixture designs," Working Papers 2013033, University of Antwerp, Faculty of Business and Economics.
    7. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2020. "Optimal designs for estimating individual coefficients in polynomial regression with no intercept," Statistics & Probability Letters, Elsevier, vol. 158(C).
    8. Idais, Osama, 2020. "A note on locally optimal designs for generalized linear models with restricted support," Statistics & Probability Letters, Elsevier, vol. 159(C).
    9. Hanen Hanna & Walter Tinsson, 2015. "A new class of designs for mixture-of-mixture experiments," Statistical Papers, Springer, vol. 56(2), pages 311-331, May.
    10. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2021. "A note on optimal designs for estimating the slope of a polynomial regression," Statistics & Probability Letters, Elsevier, vol. 170(C).
    11. Peter Goos & Bradley Jones & Utami Syafitri, 2016. "I-Optimal Design of Mixture Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 899-911, April.

    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:56:y:2015:i:1:p:105-119. 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.