Optimal Design For Additive Partially Nonlinear Models

We develop optimal design theory for additive partially nonlinear regression models, and show that D-optimal designs can be found as the products of the corresponding D-optimal designs in one dimension. For partially nonlinear models, D-optimal designs depend on the unknown nonlinear model parameters, and misspeci_cations of these parameters can lead to poor designs. Hence we generalise our results to parameter robust optimality criteria, namely Bayesian and standardised maximin D-optimality. A su_cient condition under which analogous results hold for Ds-optimality is derived to accommodate situations in which only a subset of the model parameters is of interest. To facilitate prediction of the response at unobserved locations, we prove similar results for Q-optimality in the class of all product designs. The usefulness of this approach is demonstrated through an application from the automotive industry where optimal designs for least squares regression splines are determined and compared with designs commonly used in practice. Optimal design for additive partially nonlinear models Stefanie Biedermann University of Southampton School of Mathematics Southampton SO17 1BJ UK email: [email protected] Holger Dette Ruhr-Universität Bochum Fakultät für Mathematik 44780 Bochum Germany email: [email protected] David C. Woods University of Southampton Statistical Sciences Research Institute Southampton SO17 1BJ UK email: [email protected]