Optimal designs for some selected nonlinear models

Some design aspects related to three complex nonlinear models are studied in this paper. For 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 D-optimal 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 Carathéodory׳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.