In this paper we describe the special role of moment theory for the construction of optimal designs in statistical regression models. A careful introduction in the problem of designing experiments for certain polynomial regression models is given, and it is demonstrated that the maximization of...

For the problem of percentile estimation of a quantal response curve, we determine multi-objective designs which are robust with respect to misspecifications of the model assumptions. We propose a maximin approach based on efficiencies and provide designs that are simultaneously efficient with...

In this paper the problem of designing experiments for a model which is called Monod model and is frequently used in microbiology is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research,...

In this paper we discuss a class of multiplicative algorithms for computing D-optimal designs for regression models on a finite design space. We prove amonotonicity result for a sequence of determinants obtained by the iterations,and as a consequence the procedure yields a sequence of designs...

In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A new basis for the space of natural splines is derived, and the local minimax property for these splines is used to derive two...

We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a...

The Michaelis-Menten model has and continues to be one of the most widely used models in many diverse fields. In the biomedical sciences, the model continues to be ubiquitous in biochemistry, enzyme kinetics studies, nutrition science and in the pharmaceutical sciences. Despite its wide ranging...

In this paper, we describe an adjusted method to facilitate a non-inferiority trial by a three-arm robust design. Because local optimal designs derived in Hasler et al. [2007] require knowledge about the ratios of the population variances and are not necessarily robust with respect to possible...