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Geometry of \(E\)-optimality. (English) Zbl 0780.62057

In the linear model \(y= a^ T f(x)\) the problem of calculating approximate \(E\)-optimal designs is investigated. It is well-known that in dealing with this problem the multiplicity of the minimum eigenvalue of the information matrix plays a crucial role. By introducing the concept of a sequence of generalized Elfving sets, the authors try to overcome the difficulty of the occurrence of a multiple minimum eigenvalue with, in the opinion of the reviewer, partial success. The usefulness of the method is demontrated by providing a new proof for the case of weighing designs.
Reviewer: O.Krafft (Aachen)

MSC:

62K05 Optimal statistical designs
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