Optimal minimax designs for prediction in heteroscedastic models

Journal of Statistical Planning and Inference

Volumn 69, Issue 2, 1998, Pages 371-383

  King, Joy ^a   Wong, Weng Kee ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Approximate designs; Homoscedasticity; Information matrix; Optimality criterion; Predictive variance

Indexed keywords

EID: 0032525528     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(97)00167-5     Document Type: Article

References (23)

1. Brown, L.D., Wong, W.K., 1996. An algorithmic construction of optimal minimax designs for heteroscedastic polynomial models. submitted.
2. Chaloner, K., Larntz, K., 1989. Optimal Bayesian design applied to logistic regression experiments. J. Statist. Plann. Inference 21, 191-208.
3. Cook, R.D., Fedorov, V.V., 1995. Constrained optimization of experimental design. Statistics 26, 129-178.
4. DasGupta, A., Mukhopadhyay, S., Studden, W.J., 1992. Compromise designs in heteroscedastic linear models. J. Statist. Plann. Inference 32, 363-384.
5. 1-optimal design in polynomial regression. Ann. Statist. 18, 1784-1805.
6. Fedorov, V.V., 1980. Convex design theory. Math. Operationsforsch. Statist., Ser. Statistics 11, 403-413.
7. Fox, R.L., 1971. Optimization Methods for Engineering Design. Addison-Wesley, Reading, MA.
8. Gaylor, D.W., Sweeny, H.C., 1965. Design for optimal prediction in simple linear regression. J. Amer. Statist. Assoc. 60, 205-216.
9. Hardin, R., Spane, N., 1997. A new approach to the construction of optimal designs. AT&T Bell Laboratories, DIMACS Technical Report 93-47.
10. Hoel, P.G., Levine, A., 1964. Optimum spacing and weighting in polynomial prediction. Ann. Math. Statist. 35, 1553-1560.
11. Kiefer, J., Wolfowitz, J., 1964a. Optimum extrapolation and interpolation designs I. Ann. Math. Statist. 16, 79-108.
12. Kiefer, J., Wolfowitz, J., 1964b. Optimum extrapolation and interpolation designs II. Ann. Math. Statist. 16, 295-303.
13. Kiefer, J., Wolfowitz, J., 1965. On a Theorem of Hoel and Levine on extrapolation designs. Ann. Math. Statist. 36, 1627-1655.
14. Lau, T.S., 1988. D-optimal designs on the unit q-ball. J. Statist. Plann. Inference 19, 299-315.
15. Levine, A., 1966. A problem in minimax variance polynomial extrapolation. Ann. Math. Statist. 37, 898-903.
16. v-optimal designs for multivariate polynomial regression on the q-cube. Ann. Statist. 16, 1225-1240.
17. Pazman, A., 1986. Foundations of Optimum Experimental Design. D. Reidel, Dordrecht.
18. Powell, M.J.D., 1964. An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 7, 303-307.
19. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. Cambridge University Press, Cambridge.
20. Studden, W.J., 1982. Optimal designs for weighted polynomial regression using canonical moments. Statist. Decision Theory Related Topics III 2, 335-350.
21. Vanderplaats, G.N., 1984. Numerical Optimization Techniques for Engineering Design: with Applications. McGraw-Hill.
22. Wong, W.K., 1992. A unified approach to the construction of mini-max designs. Biometrika 79, 611-620.
23. Wong, W.K., 1994. Multifactor G-optimal designs with heteroscedastic errors. J. Statist. Plann. Inference 40, 127-133.