E-OPTIMAL DESIGNS FOR LINEAR AND NONLINEAR MODELS WITH 2 PARAMETERS

A method for constructing E-optimal designs for a broad class of two-p arameter models is presented. The procedure is based on the two-dimens ional geometry of the induced design space and of the first Elfving se t and guarantees to find E-optimal designs which have exactly two poin ts of support. For E-optimal designs based on three support points, th e procedure is less clear-cut. Efficient designs based on 'essentially ' two points can be constructed using the geometry of the first Elfvin g set, but globally E-optimal designs must, at least in general, be fo und by other strategies, such as those based on symmetry consideration s, the geometry of the second Elfving set, systematic searches, or num erical methods. The methodology is illustrated by means of selected ex amples involving generalised linear models.