D-optimal designs for a two-dimensional polynomial model

Abstract

The influence of an affine transformation of the design space on the number of support points in the D-optimal design has been studied for a two-dimensional polynomial regression model. For a full rank model of degree n, a result was obtained that determines the structure of the D-optimal plan. It is proven that for a region of design space that is symmetric about zero, the optimal plan is symmetric as well. This result allows for a significant reduction in the dimensionality of the optimization problem and forms the basis of an algorithm developed by the author for finding D-optimal plans for models of incomplete rank in nonsymmetric design regions. The D-efficiency of designs concentrated at equidistant points was investigated.

Keywords:

multivariate regression models, two-dimensional polynomial regression models, D-optimal designs, D-efficiency