Designs for selected nonlinear models (Q2799897)

This paper ``is an example-based guide to optimal design for nonlinear regression models'' (from the introduction). Starting point of optimal experimental design for regression models is the Fisher information matrix which in the parameter-nonlinear case depends on the unknown regression parameter. Therefore optimal designs wrt functionals of this information matrix are only locally optimal for a given parameter. The authors present a survey of the most popular approaches for finding locally optimal designs. They start with classical methods (equivalence theorems, Elfving's theorem, covering ellipses). More general solutions can be obtained by algebraic methods [\textit{M. Yang}, Ann. Stat. 38, No. 4, 2499--2524 (2010; Zbl 1202.62103)] and by methods based on Chebyshev systems [\textit{H. Dette} and \textit{V. B. Melas}, Ann. Stat. 39, No. 2, 1266--1281 (2011; Zbl 1216.62113)]. The Michaelis-Menton model serves as illustrating example for all these approaches. Other examples can be found in a seperate chapter. Also designs for model dicrimination are mentioned. To overcome the disadvantage of locally optimality, the last chapter presents some parameter robust approaches like Bayesian designs and maximin designs.NEWLINENEWLINEFor the entire collection see [Zbl 1327.62001].