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Optimal Designs for Some Selected Nonlinear Models

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journal contribution
posted on 05.03.2018 by A.S. Hedayat, Y. Zhou, M. Yang
Some design aspects related to three complex nonlinear models are studied in this paper. For the Klimpel’s flotation recovery model, it is proved that regardless of model parameter and optimality criterion, any optimal design can be based on two design points and the right boundary is always a design point. For this model, an analytical solution for a Doptimal design is derived. For the 2-parameter chemical kinetics model, it is found that the locally D-optimal design is a saturated design. Under a certain situation, any optimal design under this model can be based on two design points. For the 2n-parameter compartment model, compared to the upper bound by Carath´eodory’s theorem, the upper bound of the maximal support size is significantly reduced by the analysis of related Tchebycheff Systems. Some numerically calculated A-optimal designs for both Klimpel’s flotation recovery model and 2-parameter chemical kinetic model are presented. For each of the three models discussed, the D-efficiency when the parameter misspecification happens is investigated. Based on two real examples from the mining industry, it is demonstrated how the estimation precision can be improved if optimal designs would be adopted. A simulation study is conducted to investigate the efficiencies of adaptive designs.




Research is supported by the U.S. National Science Foundation Grants DMS-0904125 and DMS-1306394 Research is supported by the U.S. National Science Foundation Grants DMS-0707013 and DMS-1322797


Publisher Statement

This is the author’s version of a work that was accepted for publication in Journal of Statistical Planning and Inference. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Statistical Planning and Inference. 2014. 154(1): 102-115. DOI: 10.1016/j.jspi.2014.05.005.


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