Optimal designs for regression models with possible bias

Abstract

In regression problems, departures of the true regression function from the assumed model can render experimental designs which are optimal for the assumed model inefficient. If departures from the assumed model are possible, designs need to be modified so as to protect against bias introduced by fitting the wrong model. In some instances the experimenter may be able to specify what departures from the assumed model are likely and how likely these departures may be. Such information should be useful in selecting an experimental design. In this paper we investigate such situations by assuming that a prior distribution on possible departures from the assumed model is known. A general model is given and optimal designs are obtained for some polynomial models with certain types of prior distributions over the set of all polynomials.