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Nonlinear experimental design based on the distribution of estimators. (English) Zbl 0772.62042
Optimal experimental designs are studied for nonlinear regression models with normal errors. A more sensitive approximation to the distribution of the maximum likelihood estimator of the unknown parameter vector is used than asymptotic normality. Furthermore, various types of constraints for the parameter space can be taken into consideration by adding an adequate penalty function. On the basis of this approach the mean square error is taken as optimality criterion. A stochastic approximation algorithm is proposed for calculating optimal designs with fixed size. Three examples illustrate the theory.
Reviewer: O.Krafft (Aachen)

MSC:
62K05 Optimal statistical designs
62J02 General nonlinear regression
62L20 Stochastic approximation
62E17 Approximations to statistical distributions (nonasymptotic)
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