D-optimally Lack-of-Fit-Test-efficient Designs and Related Simple Designs

Kurzfassung/Abstract

In practice it is often more popular to use a uniform than an optimal design for estimating the unknown parameters of a linear regression model. The reason is that the model can be checked by a uniform design but it cannot be checked by an optimal design in many cases. On the other hand, however, for important regression models a uniform design is not very efficient to estimate the unknown parameters. Therefore Bischoff and Miller proposed in a series of papers a compromise. It is suggested there to look for designs that are optimal with respect to a specific criterion in the class of designs that are efficient for lack-of-fit-tests. In this paper we consider the D-criterion and polynomial regression models. For polynomial regression models with degree larger than two D-optimally lack-of-fit-test-efficient designs are difficult to determine. Therefore, in this paper we determine easily to calculate and for estimating the parameters highly efficient designs that are additionally lack-of-fit-test–efficient.