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Optimal designs for free knot least squares splines

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  • Dette, Holger
  • Melas, Viatcheslav B.
  • Pepelyshev, Andrey

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.

Suggested Citation

  • Dette, Holger & Melas, Viatcheslav B. & Pepelyshev, Andrey, 2006. "Optimal designs for free knot least squares splines," Technical Reports 2006,34, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200634
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    References listed on IDEAS

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    1. Wenxin Mao & Linda H. Zhao, 2003. "Free‐knot polynomial splines with confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 901-919, November.
    2. Kaishev, V. K., 1989. "Optimal experimental designs for the B-spline regression," Computational Statistics & Data Analysis, Elsevier, vol. 8(1), pages 39-47, May.
    3. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
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