Communications for Statistical Applications and Methods

  • 제9권3호
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  • Pages.619-627
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  • 2002
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Multiple Constrained Optimal Experimental Design

  • 발행 : 2002.12.01
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초록

It is unpractical for the optimal design theory based on the given model and assumption to be applied to the real-world experimentation. Particularly, when the experimenter feels it necessary to consider multiple objectives in experimentation, its modified version of optimality criteria is indeed desired. The constrained optimal design is one of many methods developed in this context. But when the number of constraints exceeds two, there always exists a problem in specifying the lower limit for the efficiencies of the constraints because the “infeasible solution” issue arises very quickly. In this paper, we developed a sequential approach to tackle this problem assuming that all the constraints can be ranked in terms of importance. This approach has been applied to the polynomial regression model.

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참고문헌

  1. 「한국통계학회논문집」 v.7 no.1 A study on D-optimal design using the genetic algorithm 염준근;님기성
  2. Annals of Mathematical Statistics v.4 Optimal and efficient designs of experiments Atwood, C. L. https://doi.org/10.1214/aoms/1177697374
  3. Journal of the American Statistical Association v.89 On the equivalence between constrained and compound optimal designs Cook, R. D.;Wong, W. K. https://doi.org/10.2307/2290872
  4. Statistics v.26 Constrained optimization of experimental design with discussion Cook, R. D.;Fedorov, V. V. https://doi.org/10.1080/02331889508802474
  5. Ruhr-Universitat Bochum technical paper Constrained D₁-and D-optimal desings for polynomial regression Dette, H.;Franke, T.
  6. Annals of Statistics v.2 General equivalence theory for optimal designs (approximate theory) Kiefer, J. https://doi.org/10.1214/aos/1176342810
  7. Technimetrics v.11 Protection against assuming the wrong degree in polynomial regression Kussmaul, K. https://doi.org/10.2307/1266891
  8. Mathematishe Operationsforshung und Statistik v.5 Experimental planning in a class of models Lauter, E.
  9. Communications in Statistics, Part A-theory and Methods v.16 Constrained optimal designs for regression models Lee, C. M. S. https://doi.org/10.1080/03610928708829401
  10. Kybernetika v.19 On hybrid experimental design Mikulecka, J.
  11. Optimal Design of Experiments Pukelsheim, F.
  12. Journal of the American Statistical Association v.66 Optimal experimental design for polynomial regression Stigler, S. M. https://doi.org/10.2307/2283928
  13. Computational Statistics & Data Analysis v.18 Comparing robust properties of A, D. E. and G-optimal designs Wong, W. K. https://doi.org/10.1016/0167-9473(94)90161-9

피인용 문헌

  1. Hybrid Constrained Extrapolation Experimental Design vol.19, pp.1, 2012, https://doi.org/10.5351/CKSS.2012.19.1.065
  2. Some Criteria for Optimal Experimental Design at Multiple Extrapolation Points vol.27, pp.5, 2014, https://doi.org/10.5351/KJAS.2014.27.5.693