Extrapolation designs and Φp-optimum designs for cubic regression on the q-ball

This paper continues earlier work of the authors in carrying out the program discussed in Kiefer (1975), of comparing the performance of designs under various optimality criteria. Designs for extrapolation problems are also obtained. The setting is that in which the controllable variable takes on values in the q-dimensional unit ball, and the regression is cubic. Thus, the ideas of comparison are tested for a model more complex than the quadratic models discussed previously. The E-optimum design performs well in terms of other criteria, as well as for extrapolation to larger balls. A method of simplifying the calculations to obtain approximately optimum designs, is illustrated.