FINDING MAXIMUM G-CRITERION VALUES FOR CENTRAL COMPOSITE DESIGNS ON THE HYPERCUBE

For quadratic regression on the hypercube, G-efficiencies are often used in the selection process of an experimental design. To calculate a design's G-efficiency, it is necessary to maximize the prediction variance over the experimental design region. However, it is common to approximate a G-efficiency. This is achieved by calculating the prediction variances generated from a subset of points in the design space and taking the maximum to estimate the maximum prediction variance. This estimate is then applied to approximate the G-efficiency. In this paper, it will be shown that over the class of central composite designs (CCDs) on the hypercube, the prediction variance can be expressed in a closed-form. An exact value of the maximum prediction variance can then be determined by evaluating this closed-form expression over a finite subset of barycentric points. Tables of exact G-efficiencies will be presented. Design optimality criteria, quadratic regression on the hypercube, and the structures of the design matrix ($) under tilde X, ($) under tilde X'($) under tilde X, and (($) under tilde X'($) under tilde X)(-1) for any CCD will be discussed.