Abstract
In this paper we illustrate how certain design problems can be simplified by reparametrization of the response function. This alternative viewpoint provides further insights than the more traditional approaches, like minimax, Bayesian or sequential techniques. It will also improve a practitioner’s understanding of more general situations and their “classical” treatment.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Buonaccorsi JP, Iyer HK (1986) Optimal designs for ratios of linear combinations in the general linear model. Journal of Statistical Planning and Inference 13:345–356
Chaloner K, Verdinelli I (1995) Bayesian experimental design: A review. Statistical Science 10(3):273–304
Chaloner K (1989) Optimal bayesian experimental design for estimating the turning point of a quadratic regression. Communications in Statistics, Theory & Methods 18:1385–1400
Chatterjee SK, Mandal NK (1981) Response surface designs for estimating the optimal point. Calcutta Statistical Association Bulletin 30:145–169
Fedorov VV (1972) Theory of optimal experiments. Academic Press, New York
Ford I, Silvey SD (1980) A sequentially constructed design for estimating a nonlinear parametric function. Biometrika 67:381–388
Hill PDH (1980) D-optimal design for partially nonlinear models. Technometrics 16:275–276
Khuri AI (1984) A note on D-optimal design for partially nonlinear regression models. Technometrics 26(1):59–61
Mandal NK, Heiligers B (1992) Minimax designs for estimating the optimum point in a quadratic response surface. Journal of Statistical Planning and Inference 31:235–244
Mandal NK (1978) On estimation of the maximal point of a single factor quadratic response function. Calcutta Statistical Association Bulletin 27:119–125
Müller WG, Pötscher BM (1992) Batch sequential design for a nonlinear estimation problem. In: Fedorov VV, Müller WG, Vuchkov I (eds.) Model-oriented data analysis 2, Heidelberg, Physica
Müller Ch H (1995) Maximin efficient designs for estimating nonlinear aspects in linear models. Journal of Statistical Planning and Inference 44:117–132
Murty VN, Studden WJ (1972) Optimal designs for estimating the slope of a polynomial regression. Journal of the American Statistical Association 67(340):869–873
Pronzato L, Walter E (1993) Experimental design for estimating the optimum point in a response surface. Acta Applicandae Mathematicae 33:45–68
Pukelsheim F (1993) Optimal design of experiments. John Wiley & Sons, Inc., New York
Author information
Authors and Affiliations
Additional information
This paper was initiated when Werner G. Müller visited the Department of Statistics and Actuarial Sciences of the University of Iowa and his research was partially supported by the Fulbright Commission Mutual Educational Exchange Grant, the Exportakademiestipendium der Bundeswirtschafts-kammer and the OeNB-WU-Förderungspreis.
Rights and permissions
About this article
Cite this article
Fedorov, V.V., Müller, W.G. Another view on optimal design for estimating the point of extremum in quadratic regression. Metrika 46, 147–157 (1997). https://doi.org/10.1007/BF02717171
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02717171