A general approach to D-optimal designs for weighted univariate polynomial regression models.

Abstract We study the D-optimal design problem for the common weighted univariate polynomial regression model with eciency function λ. We characterize the eciency functions for which an explicit solution of the D-optimal design problem is available based on a dierential equation for the logarithmic derivative of the eciency function. In contrast to the common approach which starts with a given eciency function and derives a dierential equation for the supporting polynomial of the D-optimal design, we derive a dierential equation for the eciency function, such that an explicit solution of the D-optimal design problem is possible. The approach is illustrated for various convex design spaces and is depicted in several new examples. Also, this concept incorporates all classical eciency functions discussed in the literature so far