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D-Optimal designs for weighted polynomial regression—A functional approach

✍ Scribed by Fu-Chuen Chang

Publisher
Springer Japan
Year
2005
Tongue
English
Weight
635 KB
Volume
57
Category
Article
ISSN
0020-3157

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📜 SIMILAR VOLUMES

D-optimal designs for weighted polynomia
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✍ Fu-Chuen Chang; Ge-Chen Lin 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 672 KB

Using an Equivalence Theorem and the theory of Sturm Liouville systems, we determine the D-optimal designs for some classes of weighted polynomial regression of degree d on the interval [-1., 1]. We also show that the number of the optimal support points for such models is d+ 1. and that the optimal

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✍ Zhide Fang 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 214 KB

By utilizing the equivalence theorem and Descartes's rule of signs, we construct D-optimal designs for a weighted polynomial regression model of degree k, with speciÿc weight function w(x) = 1=(a 2 -x 2 ) , on the compact interval [ -1; 1]. The main result shows that in most cases, the number of sup

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In this work, the exact D-optimal designs for weighted polynomial regression are investigated. In Ga ke (1987, J. Statist. Planning Inference 15, 189 -204) a su cient condition has been given that Salaeveski Ä i's type of result about the exact D-optimal designs holds when sample size n is large eno

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For the regression model f k (x) = (x; x 2 ; : : : ; x k ) T on [a; 1]; -16a ¡ 1, the exact n-point D-optimal designs are proved to be ones that put mass as equally as possible among the support points of the approximate D-optimal design for f k (x) if n¿k; a = -1 and k = 2; 4, if n¿k; a¿(2 -√ 10)=6

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✍ Zhide Fang 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 119 KB

In this article we consider D-optimal designs for polynomial regression models with low-degree terms being missed, by applying the theory of canonical moments. It turns out that the optimal design places equal weight on each of the zeros of some Jacobi polynomial when the number of unknown parameter