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December2000 Constrained $D$- and $D_1$-optimal designs for polynomial regression
Holger Dette, Tobias Franke
Ann. Statist. 28(6): 1702-1727 (December2000). DOI: 10.1214/aos/1015957477

Abstract

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.

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Holger Dette. Tobias Franke. "Constrained $D$- and $D_1$-optimal designs for polynomial regression." Ann. Statist. 28 (6) 1702 - 1727, December2000. https://doi.org/10.1214/aos/1015957477

Information

Published: December2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62360
MathSciNet: MR1835038
Digital Object Identifier: 10.1214/aos/1015957477

Subjects:
Primary: 33C45 , 62K05

Keywords: $D$- and $D_1$-optimal designs , associated orthogonal polynomials , Constrined optimal designs , polynomial regression

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 6 • December2000
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