EconStor >
Technische Universität Dortmund >
Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen, Technische Universität Dortmund >
Technical Reports, SFB 475: Komplexitätsreduktion in multivariaten Datenstrukturen, TU Dortmund >

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10419/49363
  
Title:Locally E-optimal designs for exponential regression models PDF Logo
Authors:Dette, Holger
Melas, Viatcheslav B.
Pepelyshev, Andrey
Issue Date:2003
Series/Report no.:Technical Report // Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2003,37
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.
Subjects:E-optimal design
c-optimal design
exponential models
locally optimal designs
Chebyshev systems
heteroscedastic polynomial regression
Document Type:Working Paper
Appears in Collections:Technical Reports, SFB 475: Komplexitätsreduktion in multivariaten Datenstrukturen, TU Dortmund

Files in This Item:
File Description SizeFormat
379082888.psOriginal Publication497.26 kBPostscript
379082888.pdf178.42 kBAdobe PDF
No. of Downloads: Counter Stats
Download bibliographical data as: BibTeX
Share on:http://hdl.handle.net/10419/49363

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.