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Optimal designs for estimating the slope of a regression

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  • Dette, Holger
  • Melas, Viatcheslav B.

Abstract

In the common linear regression model we consider the problem of designing experiments for estimating the slope of the expected response in a regression. We discuss locally optimal designs, where the experimenter is only interested in the slope at a particular point, and standardized minimax optimal designs, which could be used if precise estimation of the slope over a given region is required. General results on the number of support points of locally optimal designs are derived if the regression functions form a Chebyshev system. For polynomial regression and Fourier regression models of arbitrary degree the optimal designs for estimating the slope of the regression are determined explicitly for many cases of practical interest.

Suggested Citation

  • Dette, Holger & Melas, Viatcheslav B., 2008. "Optimal designs for estimating the slope of a regression," Technical Reports 2008,21, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200821
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    References listed on IDEAS

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    1. Valery Fedorov & Werner Müller, 1997. "Another view on optimal design for estimating the point of extremum in quadratic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 147-157, January.
    2. Viatcheslav Melas & Andrey Pepelyshev & Russell Cheng, 2003. "Designs for estimating an extremal point of quadratic regression models in a hyperball," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 193-208, September.
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