Format:
Online-Ressource (18 S.)
,
graph. Darst.
Series Statement:
Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2008,26
Content:
We consider the common nonlinear regression model where the variance as well as the mean is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving (1952) for c-optimal designs. As in Elfving's famous characterization c-optimal designs can be described as representations of boundary points of a convex set. However, in the case where there appear parameters of interest in the variance, the structure of the Elfving set is different. Roughly speaking the Elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space. The c-optimal designs are characterized as representations of the points where the line in direction of the vector c intersects the boundary of the new Elfving set. The theory is illustrated in several examples including pharmacokinetic models with random effects. -- c-optimal design ; heteroscedastic regression ; Elfving's theorem ; pharmacokinetic models ; random effects ; locally optimal design ; geometric characterization
Note:
Parallel als Druckausg. erschienen
,
Systemvoraussetzungen: Acrobat Reader.
Language:
English
Keywords:
Arbeitspapier
;
Graue Literatur
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