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Minimax designs for optimum mixtures

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  • Pal, Manisha
  • Mandal, Nripes Kumar

Abstract

In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe [1958. Experiments with mixtures. Journal of Royal Statistical Society B 20, pp. 344-360; 1963. Simplex-centroid design for experiments with mixtures. Journal of Royal Statistical Society B 25, 235-263] first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal [2006. Optimum designs for optimum mixtures. Statistics and Probability Letters 76, 1369-1379] first attempted to find a solution to this problem using the trace criterion, assuming prior knowledge about the optimum mixing proportions. In this paper the minimax criterion has been employed to find a solution to the above problem.

Suggested Citation

  • Pal, Manisha & Mandal, Nripes Kumar, 2008. "Minimax designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 608-615, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:608-615
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    References listed on IDEAS

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    1. Valery Fedorov & Werner Müller, 1997. "Another view on optimal design for estimating the point of extremum in quadratic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 147-157, January.
    2. Pal, Manisha & Mandal, Nripes K., 2006. "Optimum designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1369-1379, July.
    3. Viatcheslav Melas & Andrey Pepelyshev & Russell Cheng, 2003. "Designs for estimating an extremal point of quadratic regression models in a hyperball," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 193-208, September.
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    Cited by:

    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. 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.
    3. Mandal, Nripes Kumar & Pal, Manisha, 2013. "Maximin designs for the detection of synergistic effects," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1632-1637.

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