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...

In the common polynomial regression of degree m we determine the design which maximizes the minimum of the D-efficiency in the model of degree m and the D-efficiencies in the models of degree m – j,…, m + k (j, k 0 given). The resulting designs allow an efficient estimation of the...

For the Michaelis-Menten model we determine designs which maximize the minimum of the D-efficiencies over a certain interval for the non-linear parameter. The best two point designs can be found explicitly and a characterization is given, when these designs are optimal within the class of all...