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Optimum mixture designs in a restricted region

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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