Marginally restricted linear-optimal designs

Abstract

In this work, we consider the problem of constructing linear-optimal designs for regression models, when some of the factors are not under the control of the experimenters. Such designs are referred to as marginally restricted (MR for brevity) linear-optimal designs. At first we make use of Fréchet derivative to the general function ø to characterize MR ø-optimal designs. Then we apply this result to prove an equivalence theorem for MR linear-optimal designs. Particularly, we discuss applications to design problems in extrapolation at a point and A -optimality, which are special cases for linear criteria. An iterative algorithm for generating MR linear-optimal designs is also presented.