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Dette, Holger
Franke, Tobias
Year of Publication: 
Series/Report no.: 
Technical Report 2000,37
In the common polynomial regression model of degree m we consider the problem of determining the D- and D1-optimal designs subject to certain constraints for the D- efficiencies in the models of degree m – j,m + j , … m + k (m > j > 0 k > 0 given). We present a complete solution of these problems, which on the one hand allow a fast computation of the constrained optimal designs and on the other hand give an answer to the question of the existence of a design satisfying all constraints. Our approach is based on a combination of general equivalence theory with the theory of canonical moments. In the case of equal bounds for the D1-efficiencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials.
Constrained optimal designs
polynomial regression
D- and D1-optimal designs
associated orthogonal polynomials
Document Type: 
Working Paper

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