D-Optimal Designs for a Two-Dimensional Polynomial Model

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