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Constrained $$D$$- and $$D_ 1$$-optimal designs for polynomial regression. (English) Zbl 1105.62360
Summary: In the common polynomial regression model of degree m we consider the problem of determining the $$D$$- and $$D_1$$-optimal designs subject to certain constraints for the $$D_1$$-efficiencies in the models of degree $$m-j$$, $$m-j+1,\dots, m + k\;(m > j\geq 0, k\geq 0 \text{ given})$$. 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 $$D_1$$-efficiencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials.

##### MSC:
 62K05 Optimal statistical designs 62J02 General nonlinear regression
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##### References:
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