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On the functional approach to optimal designs for nonlinear models

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  • Melas, Viatcheslav B.

Abstract

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.

Suggested Citation

  • Melas, Viatcheslav B., 2004. "On the functional approach to optimal designs for nonlinear models," Technical Reports 2004,13, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200413
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    References listed on IDEAS

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    1. Wong, Weng Kee & Melas, Viatcheslav B. & Dette, Holger, 2004. "Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function," Technical Reports 2004,24, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Wong, Weng Kee & Melas, Viatcheslav B. & Dette, Holger, 2004. "Locally D-optimal Designs for Exponential Regression," Technical Reports 2004,20, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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