| Abstract: | Necessary and sufficient conditions are established when a continuous design contains maximal information for a prescribed s-dimensional parameter in a classical linear model. The development is based on a thorough study of a particular dual problem and its interplay with the optimal design problem, extending partial results and earlier approaches based on differential calculus, game theory, and other programming methods. The results apply in particular to a class of information functionals which covers c-, D-, A-, L-optimality, they include a complete account of the non-differentiable criterion of E-optimality, and provide a constructive treatment of those situations in which the information matrix is singular. Corollaries pertain to the case of s out of k parameters, simultaneous optimality with respect to several criteria, multiplicity of optimal designs, bounds on their weights, and optimality which is induced by admissibility. |
