On the functional approach to optimal designs for nonlinear models - Viatcheslav B. Melas (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2004)
This paper concerns locally optimal experimental designs for non- linear regression models. It is based on the functional approach intro- duced in (Melas, 1978). In this approach locally optimal design points and weights are studied as implicitly given functions of the nonlinear parameters included in the model. Representing these functions in a Taylor series enables analytical solution of the optimal design prob- lem for many nonlinear models. A wide class of such models is here introduced. It includes, in particular,three parameters logistic distri- bution, hyperexponential and rational models. For these models we construct the analytical solution and use it for studying the e_ciency of locally optimal designs. As a criterion of optimality the well known D-criterion is considered.
Keywords: 519; nonlinear regression; experimental designs; locally optimal designs; functional approach; three parameters logistic distribution; hyperexponential models; rational models; D-criterion; implicit function theorem; Regression; Theorie; Nichtlineares Verfahren