A note on optimal designs in weighted polynomial regression for the classical efficiency functions

Gérard Antille and Holger Dette

No 2001,06, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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.

Keywords: D-optimal design; weighted polynomial regression; Rodrigues-formula; Bessel polynomials; Schrödinger equation (search for similar items in EconPapers)
Date: 2001
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/77275/2/2001-06.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200106

Access Statistics for this paper

More papers in Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().