Hybrid Constrained Extrapolation Experimental Design Kim, Young-Il; Jang, Dae-Heung;
In setting an experimental design for the prediction outside the experimental region (extrapolation design), it is natural for the experimenter to be very careful about the validity of the model for the design because the experimenter is not certain whether the model can be extended beyond the design region or not. In this paper, a hybrid constrained type approach was adopted in dealing model uncertainty as well as the prediction error using the three basic principles available in literature, maxi-min, constrained, and compound design. Furthermore, the effect of the distance of the extrapolation design point from the design region is investigated. A search algorithm was used because the classical exchange algorithm was found to be complex due to the characteristic of the problem.
Some Criteria for Optimal Experimental Design at Multiple Extrapolation Points, Korean Journal of Applied Statistics, 2014, 27, 5, 693
강명욱, 김영일 (2002). Multiple constrained optimal experimental design, The Korean Communications in Statistics, 9, 619-627.
김영일, 임용빈 (2007). Hybrid approach multiple objective experimental design, The Korean Communications in Statistics, 9, 619-627.
Atwood, C. L. (1969). Optimal and efficient designs of experiments, The Annals of Mathematical Statistics, 40, 1570-1602.
Box, G. E. P. and Draper, N. R. (1975). Robust design, Biometrika, 62, 347-352.
Cook, R. D. and Fedorov, V. V. (1995). Constrained optimization of experimental design with discussion, Statistics, 26, 129-178.
Cook, R. D. and Nachtsheim, C. J. (1982). Model-robust, linear optimal designs, Technometrics, 24, 49-54.
Cook, R. D. and Wong, W. K. (1994). On the equivalence between constrained and compound optimal designs, Journal of the American Statistical Association, 89, 687-692.
Dette, H. and Huang, M. (2000). Convex optimal designs for compound polynomial extrapolation, Annals of the Institute of Statistical Mathematics, 52, 557-573.
Dette, H. and Wong, W. K. (1996). Robust optimal extrapolation designs, Biometrika, 83, 667-680.
Fedorov, V. V. (1972). Theory of Optimal Experiments, Academic Press, Inc, New York.
Hoel, P. G. and Levine, A. (1964). Optimal spacing and weighting in polynomial prediction, Annals of Statistics, 35, 1553-1560.
Huang, M. L. and Studden, W. J. (1988). Model robust extrapolation designs, Journal of Statistical Planning and Inference, 18, 1-24.
Huang, Y. C. andWong,W. K. (1998). Multiple-objective designs, Journal of Biopharmaceutical Statistics, 8, 635-643.
Imhof, L. and Wong, W. K. (2000). A graphical method for finding maximin designs, Biometrics, 56, 113-117
Kiefer, J. and Wolfowitz, J. (1960). The equivalence of two extremum problems, Canadian Journal of Mathematics, 12, 363-366.
Kiefer, J. and Wolfowitz, J. (1964). Optimum extrapolation and interpolation designs, Annals of the Institute of Statistical Mathematics, 16, 79-108.
Kussmaul, K. (1969). Protection against assuming the wrong degree in polynomial regression, Technometrics, 11, 677-682.
Lauter, E. (1974). Experimental planning in a class of models, Mathematishe Operationsforshung und Statistik, 5, 673-708.
Lee, C. M. S. (1987). Constrained optimal designs for regression models, Communications in Statistics, Part A-theory and Methods, 16, 765-783.
Park, Y. J., Montgomery, D. C., Folwer, J. W. and Borror, C. M. (2005). Cost- constrained G-efficient response surface designs for cuboidal regions, Quality and Reliability Engineering International, 22, 121-139.
Stigler, S. M. (1971). Optimal experimental design for polynomial regression, Journal of the American Statistical Association, 66, 311-318.
Studden, W. J. (1971). Optimal designs for multivariate polynomial extrapolation, The Annals of Mathematical Statistics, 42, 828-832.
Wong,W. K. (1992). A unified approach to the construction of minimax designs, Biometrika, 79, 611-619.
Wong, W. K. (1995). A graphical approach for the construction of constrained D and L-optimal designs using efficiency plots, Journal of Statistical Computation and Simulation, 53, 143-152.
Yum, J. K. and Nam, K. S. (2000). A study on D-optimal design using the genetic algorithm, The Korean Communications in Statistics, 7, 357-366.