When product type experimental design is optimal? Brief survey and new results (Q1205144)

The authors considered a classical linear regression model and found conditions to be imposed and a criterion under which one can find an optimal design \(\xi\) in a certain class of designs. They considered product designs for multiplicative and additive multivariate models. A number of models, especially polynomial, polynomial plus trigonometric regression and mixed models have been considered and conditions for \(D\)-, \(L\)- and \(\psi\)-optimality, etc. have been derived. The authors have chosen very general models in vector and matrix form with Kronecker product notation and their applications in practical situations like factorial experiments have been shown as a particular case. This paper needs very good background in matrix theory.