A Study of D-optimal Designs Efficiency for Polynomial Regression

In this paper we present a numerical study of D-efficiency for a polynomial regression of known or unknown degree. A rule of the degree choice, based on D-efficiency is proposed for classical efficiency functions. We study the conjecture that the less central a design point is the greater its influence on D-efficiency is. Perturbations of design points show that this conjecture is only true for some efficiency functions. For non exponential efficiency functions the departure from the model is more important than the departure from the optimal design. We also introduce a concept of higher-order D-optimal designs and compare them in the case of unknown regression degree with uniform designs (studied by Huber) and the designs obtained by using prior probabilities. Our conclusion is that the higher-order D-optimal designs are more efficient that the uniform ones. Generally they are less efficient than Lauter-optimal designs for weighted polynomial regression but they need no prior information.