On D-optimality of exact linear regression designs with minimum support (Q1082756)

For some classical regression models, a sufficient condition for D- optimal exact designs \(\xi^*_ n\) with a given total number n of observations from D-optimal approximate design \(\xi^*\) with minimum support is obtained by rounding off its weights to integral multiples of 1/n. For some specific models, a necessary condition for D-optimality of a given exact design is also proved. The conditions are expressed in terms of information matrices and minimum support points. D-optimal exact designs for five specific polynomial regressions are also dealt with. The author gives three examples as well. One interesting open problem is left for further investigation.