A graphical method for finding maximin efficiency designs

Biometrics

Volumn 56, Issue 1, 2000, Pages 113-117

  Imhof, Lorens ^a   Wong, Weng Kee ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Compound optimal designs; Concave functions; Multiple objective optimal designs

Indexed keywords

GRAPHIC METHODS; OPTIMAL SYSTEMS;

COMPOUND OPTIMAL DESIGN; CONCAVE FUNCTION; DESIGNING AN EXPERIMENT; GRAPHICAL METHODS; MAXIMIN; MULTIPLE-OBJECTIVE OPTIMAL DESIGN; MULTIPLE-OBJECTIVES; OPTIMAL DESIGN; OPTIMALITY CRITERIA;

EFFICIENCY;

ARTICLE; EXPERIMENT; MATHEMATICAL MODEL; NONLINEAR SYSTEM; PRODUCTIVITY; SCIENTIFIC LITERATURE; STATISTICS;

EID: 0034021940     PISSN: 0006341X     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0006-341X.2000.00113.x     Document Type: Article

References (31)

1. Atkinson, A. C. and Bogacka, B. (1997). Compound D- and Ds-optimum designs for determining the order of a chemical reaction. Technometrics 39, 347-356.
2. Atkinson, A. C. and Donev, A. N. (1992). Optimum Experimental Designs. New York: Oxford University Press.
3. Atkinson, A. C. and Haines, L. M. (1996). Designs for nonlinear and generalized linear models. In Handbook of Statistics, Volume 13, S. Ghosh and C. R. Rao (eds), 437-475. New York: Elsevier Science.
4. Chaloner, K. and Larntz, K. (1989). Optimal Bayesian design applied to logistic regression experiments. Journal of Statistical Planning and Inference 21, 191-208.
5. Chernoff, H. (1953). Locally optimal designs for estimating parameters. The Annals of Mathematical Statistics 24, 586-602.
6. Cook, R. D. and Wong, W. K. (1994). On the equivalence of constrained and compound optimal designs. Journal of the American Statistical Association 89, 687-692.
7. Cox, C. P. (1972). On estimating relative potency from quadratic log-dose response relationships. Biometrics 28, 875-881.
8. Efron, B. and Tibshirani, R. (1991). Statistical data analysis in the computer age. Science 253, 875-395.
9. Haines, L. M. (1995). A geometric approach to optimal design for one-parameter non-linear models. Journal of the Royal Statistical Society, Series B 57, 575-598.
10. Huang, Y. C. (1996). Multiple-objective optimal designs. Ph.D. dissertation, Department of Biostatistics, School of Public Health, University of California at Los Angeles.
11. Huang, Y. C. and Wong, W. K. (1998). Multiple-objective designs. Journal of Biopharmaceutical Statistics 8, 635-643.
12. Kalish, L. A. (1990). Efficient design for estimation of median lethal dose and quantal dose response curves. Biometrics 46, 737-748.
13. Kiefer, J. (1959). Optimum experimental designs. Journal of the Royal Statistical Society, Series B 21, 272-319.
14. Kiefer, J. (1975). Optimal design: Variation in structure and performance under change of criterion. Biometrika 62, 277-288.
15. King, J. and Wong, W. K. (1998). Optimal minimax designs for prediction in heteroscedastic models. Journal of Statistical Planning and Inference 69, 371-383.
16. Laeuter, E. (1976). Optimal multipurpose designs for regression models. Mathematische Operationsforschung und Statistik 7, 51-68.
17. Lee, C. M. S. (1987). Constrained optimal designs for regression models. Communications in Statistics, Theory, and Methods 16, 765-783.
18. Lee, C. M. S. (1988). Constrained optimal designs. Journal of Statistical Planning and Inference 18, 377-389.
19. Mueller, C. and Pazman, A. (1998). Applications of necessary and sufficient conditions for maximin efficient designs. Metrika 48, 1-19.
20. O'Brien, T. E. (1994). A new robust design strategy for sigmoidal models based on model nesting. In CompStat 1994, R. Dutter and W. Grossmann (eds), 97-102. Heidelberg: Physica-Verlag.
21. O'Brien, T. E. (1996). Robust design strategies for nonlinear regression models. In Versuchsplanung in der Industrie, H. Toutenberg and R. (eds), 41-52. Munich: Prentice Hall.
22. Pazman, A. (1986). Foundations of Optimum Experimental Design. Dordrecht: Reidel.
23. Pronzato, L. and Walter, E. (1988). Robust experiment design via maximin optimization. Mathematical Biosciences 89, 161-176.
24. Schwabe, R. (1997). Maximin efficient designs: Another view at D optimality. Statistics and Probability Letters 35, 109-114.
25. Silvey, S. D. (1980). Optimal Design. London: Chapman and Hall.
26. Spears, F. M., Brown, B. W., and Atkinson, E. N. (1997). The effect of incomplete knowledge of parameter values on single- and multiple-stage designs for logistic regression. Biometrics 53, 1-10.
27. Wong, W. K. (1992). A unified approach to the construction of mini-max designs. Biometrika 79, 611-619.
28. Wong, W. K. (1995). A graphical approach for constructing constrained D and L-optimal designs using efficiency plots. Journal of Statistical Simulation and Computation 53, 143-152.
29. Wong, W. K. and Cook, R. D. (1993). Heteroscedastic G-optimal designs. Journal of the Royal Statistical Society, Series B 55, 871-880.
30. Zhu, W. and Wong, W. K. (1998). Multiple-objective designs in dose-response experiments. In New Developments and Applications in Experimental Design, Volume 34, IMS Lecture Notes - Monograph Series, N. Flornoy, W. Rosenberger, and W. K. Wong (eds), 73-82. Hayward, California: Institute of Mathematical Sciences.
31. Zhu, W., Ahn, H., and Wong, W. K. (1998). Multiple-objective optimal designs for the logit model. Communications in Statistics - Theory and Methods 27, 1581-1592.