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Locally E-optimal designs for exponential regression models

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

Abstract

In this paper we investigate locally E- and c-optimal designs for exponential regression models of the form _k i=1 ai exp(??ix). We establish a numerical method for the construction of efficient and locally optimal designs, which is based on two results. First we consider the limit ?i ? ? and show that the optimal designs converge weakly to the optimal designs in a heteroscedastic polynomial regression model. It is then demonstrated that in this model the optimal designs can be easily determined by standard numerical software. Secondly, it is proved that the support points and weights of the locally optimal designs in the exponential regression model are analytic functions of the nonlinear parameters ?1, . . . , ?k. This result is used for the numerical calculation of the locally E-optimal designs by means of a Taylor expansion for any vector (?1, . . . , ?k). It is also demonstrated that in the models under consideration E-optimal designs are usually more efficient for estimating individual parameters than D-optimal designs.

Suggested Citation

  • Dette, Holger & Melas, Viatcheslav B. & Pepelyshev, Andrey, 2003. "Locally E-optimal designs for exponential regression models," Technical Reports 2003,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200337
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    1. Dette, Holger & Melas, Viatcheslav B. & Pepelyshev, Andrey, 2002. "Optimal designs for a class of nonlinear regression models," Technical Reports 2002,64, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Dette, Holger & Martinez Lopez, Ignacio & Ortiz Rodriguez, Isabel M. & Pepelyshev, Andrey, 2004. "Efficient design of experiment for exponential regression models," Technical Reports 2004,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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    1. Holger Dette & Viatcheslav Melas & Andrey Pepelyshev, 2006. "Local c- and E-optimal Designs for Exponential Regression Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 407-426, June.

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