A relaxation procedure for calculating (G–)minimax optimal designs |
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Authors: | Alexander Begun and Wilfried Seidel |
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Institution: | (1) Fachbereich WOW Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, 22039 Hamburg |
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Abstract: | Summary:
In nonlinear statistical models, standard optimality functions for experimental
designs depend on the unknown parameters of the model. An appealing and robust
concept for choosing a design is the minimax criterion. However, so far, minimax optimal
designs have been calculated efficiently under various restrictive conditions only. We
extend an iterative relaxation scheme originally proposed by Shimizu and Aiyoshi (1980)
and prove its convergence under very general assumptions which cover a variety of situations
considered in experimental design. Application to different specific design criteria
is discussed and issues of practical implementation are addressed. First numerical results
suggest that the method may be very efficient with respect to the number of iterations
required.*Supported by a grant from the Deutsche Forschungsgemeinschaft. We are grateful to
a referee for his constructive suggestions. |
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Keywords: | Minimax problems nonlinear experimental design robust optimal design Gamma– minimax D– optimality |
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