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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.

62K05 Optimal statistical designs
62J02 General nonlinear regression
Full Text: DOI
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