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...

n.a.

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,...

We determine optimal designs for some regression models which are frequently used for describing 3D shapes. These models are based on a Fourier expansion of a function defined on the unit sphere in terms of spherical harmonic basis functions. In particular it is demonstrated that the uniform...

In this paper we investigate locally E- and c-optimal designs for exponential regression models of the form _k i=1 ai exp(??ix). We establish a numerical method for the construction of efficient and locally optimal designs, which is based on two results. First we consider the limit ?i ? ? and...

In the common Fourier regression model we investigate the optimal design problem for estimating pairs of the coefficients, where the explanatory variable varies in the interval [¡¼; ¼]. L-optimal designs are considered and for many important cases L-optimal designs can be found explicitly,...

We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumption. An extended model, called EMAX model is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis- Menten model for a specific...

We study locally D-optimal designs for some exponential models that are frequently used in the biological sciences. The model can be written as an algebraic sum of two or three exponential terms. We show that approximate locally D-optimal designs are supported at a minimal number of points and...

The Monod model is a classical microbiological model much used in microbiology, for example to evaluate biodegradation processes. The model describes microbial growth kinetics in batch culture experiments using three parameters: the maximal specific growth rate, the saturation constant and the...

In the common Fourier regression model we determine the optimal designs for estimating the coefficients corresponding to the lower frequencies. An analytical solution is provided which is found by an alternative characterization of c-optimal designs. Several examples are provided and the...