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 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...

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 [¡ơ; ơ]. L-optimal designs are considered and for many important cases L-optimal designs can be found explicitly,...

If a model is fitted to empirical data, bias can arise from terms which are not incorporated in the model assumptions. As a consequence the commonly used optimality criteria based on the generalized variance of the estimate of the model parameters may not lead to efficient designs for the...

In the common linear regression model we consider the problem of designing experiments for estimating the slope of the expected response in a regression. We discuss locally optimal designs, where the experimenter is only interested in the slope at a particular point, and standardized minimax...

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...

In the common trigonometric regression model we investigate the optimal design problem for the estimation of the individual coefficients, where the explanatory variable varies in the interval [-a ,a] ; 0 a t. It is demonstrated that the structure of the optimal design depends sensitively on...

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...