IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200337.html
   My bibliography  Save this paper

Locally E-optimal designs for exponential regression models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/49363/1/379082888.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb475:200337. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/isdorde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.