Optimal designs for free knot least squares splines

Holger Dette, Viatcheslav B. Melas and Andrey Pepelyshev

No 2006,34, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: In this paper D-optimal designs for free knot least squares spline estimation are investigated. In contrast to most of the literature on optimal design for spline regression models it is assumed that the knots of the spline are also estimated from the data, which yields to optimal design problems for nonlinear models. In some cases local D-optimal designs can be found explicitly. Moreover, it is shown that the points of minimally supported D-optimal designs are increasing and real analytic functions of the knots and these results are used for the numerical construction of local D-optimal designs by means of Taylor expansions. In order to obtain optimal designs which are less sensitive with respect to a specification of the unknown knots a maximin approach is proposed and standardized maximin D-optimal designs for least square splines with estimated knots are determined in the class of all minimally supported designs.

Keywords: Free knot least squares splines; D-optimal designs; nonlinear models; local optimal designs; robust designs; saturated designs (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/22678/1/tr34-06.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:sfb475:200634

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 ().