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Statistical Decision Theory and Related Topics II
- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/BF00995494
- Publisher site
- See Article on Publisher Site
Abstract
The problem of optimal experimental design for response optimization is considered. The optimal point (control)x * of a response surface is to be determined by estimating the response parametersθ from measurements performed at design pointsx i,i=1,...,N. Classical sequential approaches for choosing thex i's are recalled. A loss function related to the issue of response optimization is used to define control-oriented design criteria. The design policies differ depending on whether least-squares or minimum risk estimation is used to estimateθ. Connections between various criteria suggested in the literature are exhibited. Special attention is given to quadratic model responses. Most approaches presented assume that the response is correctly described by a given parametric function over the region of interest. Possible deterministic departures from this function raise the problem of model robustness, and the literature on the subject is briefly surveyed.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 31, 2004