In this paper the estimation problem and the problem of designing experiments in a nonlinear regression model, used in microbiology, are studied. The model is called Monod model, defined imlicitly by a differential equation for the regression function and has numerous applications in microbial...

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 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 D-optimal designs for free knot least squares spline estimation are investigated. In contrast to most of the literature on optimal design for spline regression models it is assumed that the knots of the spline are also estimated from the data, which yields to optimal design...

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...

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 this paper the optimal design problem for the estimation of the individual coefficients in a polynomial regression on an arbitrary interval [a, b] (- inf. a b inf) is considered. Recently, Sahm (2000) demonstrated that the optimal design is one of four types depending on the symmetry...