Designs for estimating an extremal point of quadratic regression models in a hyperball

Metrika

Volumn 58, Issue 2, 2003, Pages 193-208

  Melas, Viatcheslav B ^a   Pepelyshev, Andrey ^a   Cheng, Russell C H ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Equivalence theorems; Estimating of an extremum point; Quadratic regression model; Truncated locally D optimal designs

Indexed keywords

EID: 17444410261     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001840200237     Document Type: Article

References (17)

1. Box GEP, Wilson KB (1951) On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society ser. B 13:1-38
2. Chaloner K (1989) Optimal bayesian experimental design for estimation the turning point of a quadratic regression. Communication of Statistics, Theory and Methods 18:1385-1400
3. Chatterjee SK, Mandal NK (1981) Response surface designs for estimating the optimal point. Calcutta Statistical Association Bulletin 30:145-169
4. Cheng RCH, Melas VB, Pepelyshev AN (2000) Optimal design for evaluation of an extremum point. In: Atkinson A, Bogacka B, Zhigljavsky A (eds) Optimum Design 2000. Kluwer, 15-24
5. Dette H, Melas VB, Pepelyshev AN (2001) Optimal designs for estimating individual coefficients in polynomial regression - a functional approach. Preprint, Ruhr-Universität Bochum, http://www.ruhr-uni-bochum.de/ mathematik3/preprint.htm
6. Ermakov SM et al. (1983) Mathematical theory of experimental design. Moscow, Nauka (Russian)
7. Fedorov W, Müller WC (1997) Another view on optimal design for estimating the point of extremum in quadratic regression. Metrika 46:147-157
8. Ford I and Silvey SD (1980) A sequentially constructed design for estimating a nonlinear parameter function. Biometrika 67:381-388.
9. Karlin S, Studden W (1966) Tchebysheff systems: with application in analysis and statistics. New York: Wiley
10. 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
11. Mandal NK (1978) On estimation of the maximal point of single factor quadratic response function. Calcutta Statistical Association Bulletin 27:119-125
12. Müller WG, Pötscher BM (1992) Batch sequential design for a nonlinear estimation problem. In: Fedorov W, Müller WC, Vuchkov I (eds) Model-Oriented Data Analysis 2, Heidelberg. Physica
13. Müller ChH (1995) Maximin efficient designs for estimating nonlinear aspects in linear models. Journal of Statistical Planning and Inference 44:117-132
14. Müller ChH, Pázman A (1998) Applications of necessary and sufficient conditions for maximum efficient design. Metrika 48:1-19
15. Pronzato L, Walter E (1993) Experimental design for estimating the optimum point in a response surface. Acta Applicandae Mathematicae 33:45-68
16. Pukelsheim F (1993) Optimal design of experiments. Wiley, New York
17. Silvey SD, Titterington DM (1973) A geometric approach to optimal design theory. Biometrica 60:21-32