Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/77275
Authors: 
Antille, Gérard
Dette, Holger
Year of Publication: 
2001
Series/Report no.: 
Technical Report, SFB 475: Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2001,06
Abstract: 
In this note we consider the D-optimal design problem for the heteroscedastic polynomial regression model. Karlin and Studden (1966a) found explicit solutions for three types of efficiency functions. We introduce two ‘new’ functions to model the heteroscedastic structure, for which the D-optimal designs can also be found explicitly. The optimal designs have equal masses at the roots of generalized Bessel polynomials and Jacobi-polynomials with complex parameters. It is also demonstrated that there exist no other efficiency functions such that the supporting polynomial of the D-optimal design satisfies a generalized Rodrigues-formula.
Subjects: 
D-optimal design
weighted polynomial regression
Rodrigues-formula
Bessel polynomials
Schrödinger equation
Document Type: 
Working Paper

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