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D-optimal design for Becker's minimum polynomial

Author

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  • Hilgers, Ralf-Dieter

Abstract

Becker's minimum polynomial (e.g. Becker, 1968, J. Roy. Statist. Soc. Ser. B 30, 349-358.) of order [nu] on the (unit) q-simplex including the minimum functions over all subsets of at most [nu][less-than-or-equals, slant]q variables is considered. D-optimal approximate designs for this model are shown to be supported on the barycenters. The minimum support design concentrated on the barycenters corresponding to the regression functions is optimal for [nu]=q whereas it fails to be optimal for [nu]

Suggested Citation

  • Hilgers, Ralf-Dieter, 2000. "D-optimal design for Becker's minimum polynomial," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 175-179, August.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:2:p:175-179
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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.
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    Cited by:

    1. Zhang, Chongqi & Wong, Weng Kee, 2013. "Optimal designs for mixture models with amount constraints," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 196-202.
    2. Aggarwal, M. L. & Sarin, V. & Singh, Poonam, 2002. "Optimal orthogonal designs in two blocks for Becker's mixture models in three and four components," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 385-396, October.

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