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Pseudo-Bayesian A-optimal designs for estimating the point of maximum in component-amount Darroch–Waller mixture model

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  • Mandal, N.K.
  • Pal, Manisha
  • Aggarwal, M.L.

Abstract

In the analysis of experiments with mixture, quadratic models have been widely used. Several authors considered finding optimum designs for the estimation of the parameters of the model. The optimum designs for the estimation of optimum mixing proportions in Scheffé’s quadratic mixture model has been studied by Pal and Mandal (2006) and Mandal et al. (2008a,b) using a pseudo-Bayesian approach. In this paper, we consider an additive quadratic mixture model, proposed by Darroch and Waller (1985), when the amount of mixture is taken into account, and obtain the A-optimal designs for the estimation of optimum proportions, adopting the approach of Pal and Mandal (2006). We show that, besides other support points, the origin and the vertices of the simplex are necessarily the support points of the optimum design.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1088-1094
    DOI: 10.1016/j.spl.2012.02.011
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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. 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.
    3. Pal, Manisha & Mandal, Nripes K., 2006. "Optimum designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1369-1379, July.
    4. 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. Walker, Stephen G., 2016. "Bayesian information in an experiment and the Fisher information distance," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 5-9.

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