Optimality criteria for design in nonlinear models with constraints (Q2913247)

A new class of global optimality criteria for designs in nonlinear regression models with constraints is discussed. The classical global optimality criteria (such as, e.g.,~D-optimality, A-optimality or E-optimality) are based on convex function of the (asymptotic) information matrix. However, they are not directly applicable in situations with constrained parameters. The author suggests a new class of optimality criteria based on the (asymptotic) covariance matrix of the parameter estimators under the given constraints. The situation is even more complicated if, in particular, a D-optimality criterion is considered, as the covariance matrix is not of a full rank. In this situation, the author suggests to consider a simple criterion based on a function of the covariance matrix and shows that it is equivalent to consider an equivalent (reparametrized) model without restrictions on the parameters. Based on the new optimality criteria and based on the well-known equivalence theorem the author presents the necessary and sufficient conditions for an optimal design (with respect to the chosen optimality criteria).