E-optimal designs for linear and nonlinear models with two parameters

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Abstract
A method for constructing E-optimal designs for a broad class of two-parameter models is presented. The procedure is based on the two-dimensional geometry of the induced design space and of the first Elfving set and guarantees to find E-optimal designs which have exactly two points of support. For E-optimal designs based on three support points, the procedure is less clear-cut. Efficient designs based on ‘essentially’ two points can be constructed using the geometry of the first Elfving set, but globally E-optimal designs must, at least in general, be found by other strategies, such as those based on symmetry considerations, the geometry of the second Elfving set, systematic searches, or numerical methods. The methodology is illustrated by means of selected examples involving generalised linear models.

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