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 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 y(i) = g(ti) + a (ti) ei , i=1….,n with i.i.d - noise and nonrepeatable design points ti we consider the problem of choosing an optimal design for the estimation of the regression function g. A minimax approach is adopted which searches for designs...

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...

In this note we consider the D-optimal design problem for the heteroscedastic polynomial regression model. Karlin and Studden (1966a) found explicit solutions for three types of efficiency functions. We introduce two ‘new’ functions to model the heteroscedastic structure, for which the...