Optimal Minimum Bias Designs for Model Discrimination

• Park, Joong-Yang (Department of Statistics and Information and Communication Research Center, Gyeongsang National University)
• Published : 1998.08.01

Abstract

Designs for discriminating between two linear regression models are studied under $\Lambda$-type optimalities maximizing the measure for the lack of fit for the designs with fixed model inadequacy. The problem of selecting an appropriate $\Lambda$-type optimalities is shown to be closely related to the estimation method. $\Lambda$-type optimalities for the least squares and minimum bias estimation methods are considered. The minimum bias designs are suggested for the designs invariant with respect to the two estimation methods. First order minimum bias designs optimal under $\Lambda$-type optimalities are then derived. Finally for the case where the lack of fit test is significant, an approach to the construction of a second order design accommodating the optimal first order minimum bias design is illustrated.

References

1. Biometrika v.59 Planning experiments to detect inadequate regression models Atkinson, A.C.
2. Biometrika v.62 The design of experiments for discriminating between two rival models Atkinson, A.C.;Fedorov, V.V.
3. Biometrika v.62 Optimal design: Experiments for discriminating between several models Atkinson, A.C.;Fedorov, V.V.
4. Biometrika v.50 The choice of a second order rotatable designs Box, G.E.P.;Draper, N.R.
5. Journal of the American Statistical Association v.68 Minimum bias approximation of a general regression model Cote, R.;Manson, R.;Hader, R.J.
6. Biometrika v.79 A new look at experimental design robustness DeFeo, P.;Myers, R.H.
7. Journal of the American Statistical Association v.72 All-bias designs for spline functions joined at the axes Draper, N.R.;Guttman, I.;Lipow, P.
8. Technometrics v.30 Designs for minimum bias estimation Draper, N.R.;Sanders, E.R.
9. Journal of the American Statistical Association v.73 Optimal experimental design in two dimensions using minimum bias estimation Evans, J.W.;Manson, A.R.
10. Biometrika v.73 Duality of optimal designs for model discrimination and parameter estimation Fedorov, V.;Khabarov, V.
11. Journal of Statistical Planning and Inference v.1 Comparison of designs for quadratic regression on cubes Galil, Z.;Kiefer, J.
12. Biometrika v.65 Design criteria for detecting model inadequacy Jones, E.R.;Mitchell, T.J.
13. Technometrics v.11 Minimum bias estimation and experimental design for response surfaces Karson, M.J.;Manson, A.R.;Hader, R.J.
14. Communications in Statistics v.4 Design criteria and minimum bias estimation Karson, M.J.;Spurill, M.L.
15. Communications in Statistics-Theory and Method v.A6 Secondary design considerations for minimum bias estimation Khuri, A.I.;Cornell, J.R.
16. Technometrics v.17 A generalization of the response surface mean square error criterion with a specific application to the slope Myers, R.H.;Lahoda, S.J.
17. Communications in Statistics-Theory and Method v.19 Designs for estimating the difference between two responses Park, J-Y.
18. Technometrics v.15 Secondary criterion in the selection of minimum bias designs in two variables Thompson, W.O.