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 Γ i's type of result about the exact D-optimal designs holds when sample size n is large eno
Exact and approximate D-optimal designs in polynomial regression
β Scribed by Maximilian Happacher
- Publisher
- Springer
- Year
- 1995
- Tongue
- English
- Weight
- 320 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0026-1335
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π SIMILAR VOLUMES
For the regression model f k (x) = (x; x 2 ; : : : ; x k ) T on [a; 1]; -16a Β‘ 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 nΒΏk; a = -1 and k = 2; 4, if nΒΏk; aΒΏ(2 -β 10)=6
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
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 speciΓΏc 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
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