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Original Articles

A-optimal designs for optimum mixture in an additive quadratic mixture model

, &
Pages 265-276 | Received 08 Aug 2009, Accepted 25 Apr 2016, Published online: 27 Dec 2016

References

  • SchefféH. Experiments with mixtures. J R Statist Soc B. 1958;20:344–360.
  • Darroch JN, Waller J. Additivity and interaction in three-component experiments with mixtures. Biometrika. 1985;72:153–163. doi: 10.1093/biomet/72.1.153
  • Snee RD. Developing blending models for gasoline and other mixtures. Technometrics. 1981;23:119–130. doi: 10.1080/00401706.1981.10486254
  • Snee RD. Techniques for the analysis of mixture data. Technometrics. 1973;15:517–528. doi: 10.1080/00401706.1973.10489078
  • Kiefer J. Optimum designs in regression problems, II. Ann Math Statist. 1961;32:298–325. doi: 10.1214/aoms/1177705160
  • Atwood CL. Optimal and efficient designs of experiments. Ann Math Statist. 1969;40:1570–1602. doi: 10.1214/aoms/1177697374
  • Galil Z, Kiefer J. Comparison of simplex designs for quadratic mixture models. Technometrics. 1977;19:445–453. doi: 10.1080/00401706.1977.10489584
  • Chan L-Y, Guan Y-N, Zhang C-Q. A-optimal design for an additive quadratic mixture model. Statist Sin. 1998;8:979–990.
  • Draper NR, Pukelsheim F. Kiefer ordering of simplex designs for first and second degree mixture models. J Statist Plan Inference. 1999;79:325–348. doi: 10.1016/S0378-3758(98)00263-8
  • Pal M, Mandal NK. Optimum designs for optimum mixtures. Statist Probab Lett. 2006;76:1369–1379. doi: 10.1016/j.spl.2006.02.007
  • Mandal NK, Pal M. Optimum mixture design using deficiency criterion. Commun Statist Theory Methods. 2008;37(10):565–575. doi: 10.1080/03610920701712957
  • Mandal NK, Pal M, Sinha BK, Das P. Optimum mixture designs: a pseudo-Bayesian approach. J Ind Soc Agric Statist. 2008;62(2):174–182.
  • Mandal NK, Pal M, Sinha BK, Das P. Optimum mixture designs under constraints on mixing components. Statist. Appl. 2008;6(1 & 2):189–205. (New Series).
  • Pal M, Mandal NK. Optimum mixture design via equivalence theorem. J Combin Inf Syst Sci. 2007;32(2):107–126.
  • Pal M, Mandal NK. Minimax designs for optimum mixtures. Statist Probab Lett. 2008;78(6):608–615. doi: 10.1016/j.spl.2007.09.022
  • Pal M, Mandal NK. Optimum designs for estimation of optimum point under cost constraint. J Appl Statist. 2009;36(9):999–1008. doi: 10.1080/02664760802582264
  • Chatterjee SK, Mandal NK. Response surface designs for estimating the optimal point. Calcutta Stat Assoc Bull. 1981;30:145–170. doi: 10.1177/0008068319810307
  • Mandal NK, Heilligers B. Minimax designs for estimating the optimum point in a multifactor experiment. J Stat Plan Inf. 1992;31:234–244. doi: 10.1016/0378-3758(92)90032-N
  • Cheng RCH, Melas VB, Pepelyshev AN. Optimal designs for the evaluation of an extremum point. In: Atkinson VB, Bogacka B, Zhigljavsky A, editors. Optimum design 2000. Dordrecht: Kluwer Academic Publishers; 2001. p. 15–24. doi: 10.1007/978-1-4757-3419-5_2
  • Fedorov VV, Müller WG. Another view on optimal design for estimating the point of extremum in quadratic regression. Metrika. 1997;46:147–157. doi: 10.1007/BF02717171
  • Peterson JJ, Cahya S, del Castillo E. A general approach to confidence regions for optimal factor levels. Biometrics. 2002;58:134–143. doi: 10.1111/j.0006-341X.2002.00422.x
  • Cahya S, del Castillo E, Peterson JJ. Computation of confidence region for optimal factor levels in constrained response surface problems. J Comput Graph Statist. 2004;13:499–518. doi: 10.1198/1061860043443
  • Chaloner K, Verdinelli I. Bayesian experimental design: a review. Statist Sci. 1995;10:273–304. doi: 10.1214/ss/1177009939
  • Kiefer J. General equivalence theory for optimum designs (approximate theory). Ann Statist. 1974;2(5): 849–879. doi: 10.1214/aos/1176342810
  • Fedorov VV, Hackl P. Model-oriented design of experiments. Lecture notes in statistics. New York (NY): Springer-Verlag; 1997.
  • Morrison DF. Multivariate statistical methods. Tokyo: McGraw Hill; 1976.

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