Algorithmen zur Errechnung von Versuchsplänen mit unkontrollierbaren erklärenden Variablen

ÖAD Österreichischer akademischer Austauschdienst

In the classical theory of optimal design for linear models it is usually assumed that all independent variables can be controlled completely throughout the design space. Nevertheless, in many areas of application it is common to find that some of the independent variables are not subject to the control of the practitioner. Cook and Thibodeau (1980) discuss the problem of obtaining approximate D-optimal designs when the design space is a product space and when the carriers associated with one marginal are not subject to control. Huang and Hsu (1993) and Huang and Chang (1995) extend some of the results provided by Cook and Thibodeau(1980) to other criteria giving some algorithms. Nachtsheim (1989) provides equivalence theorems and algorithms for D- and Ds--optimality. These works assume that the uncontrolled variables have known values before the experiment is performed.

The aim of this research is to tackle the more general problem of obtaining Ħ-optimal approximate designs for regression models when the values of some of the variables that are not under control are only known in advance through a general conditional probability distribution. This distribution may be given by the practitioner since he could know ``what is about to happen'' with a/some variable/s x1 for specific values of other variable/s x2.

From a practical point of view the construction of optimal designs for regression models when the design space is a product space and some of the variables are not under the control of the practitioner an equivalence theorem has to be proved in order to produce algorithms for the computation of optimal designs. Then a computer code should be given.