On a mixture of the \(D\)- and \(D_ 1\)-optimality criterion in polynomial regression. (English) Zbl 0768.62056
Summary: We consider a mixture of the \(D_ 1\)-optimality criterion (minimizing the variance of the estimate for the highest coefficient) and the \(D\)- optimality criterion (minimizing the volume of the ellipsoid of concentration for the unknown parameter vector) in the polynomial regression model of degree \(n\in \mathbb{N}\). The mixture is defined as a weighted product of both optimality criteria and explicit solutions are given for the proposed criterion. The derived designs have excellent efficiencies compared to the \(G\)-, \(D\)- and \(D_ 1\)-optimal design.
This is illustrated in some examples for polynomial regression of lower degree. The optimal designs are calculated using the theory of canonical moments. Further applications are given in the field of model robust designs for polynomial regression models where only an upper bound for the degree of the polynomial regression model is known by the experimenter before the experiments are carried out.
This is illustrated in some examples for polynomial regression of lower degree. The optimal designs are calculated using the theory of canonical moments. Further applications are given in the field of model robust designs for polynomial regression models where only an upper bound for the degree of the polynomial regression model is known by the experimenter before the experiments are carried out.
MSC:
| 62K05 | Optimal statistical designs |
| 62J02 | General nonlinear regression |
| 62J05 | Linear regression; mixed models |
Keywords:
mixture of optimality criteria; ultraspherical polynomials; \(D\)- optimality criterion; polynomial regression model; explicit solutions; canonical moments; model robust designsReferences:
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