Constrained optimal designs
Consider the usual setting of optimal design theory with a design \(\xi\) given by a discrete measure \(\xi =\{P_ 1,P_ 2,...,P_ n\}\) with support \(\{x_ 1,x_ 2,...,x_ n\}\). Let M(\(\xi)\) be the information matrix of a design \(\xi\) and assume M(\(\xi)\) to be non-singular. The paper tackles the following constrained optimal design problem: Minimize the functional \(\phi\) (M(\(\xi)\)) over the set of all designs with non- singular information matrices subject to \(\phi_ iM(\xi))\leq 0\), \(i=1,2,...,m\), where \(\phi_ 1,\phi_ 2,...,\phi_ m\) are m specified functionals on M(\(\xi)\). Under a set of assumptions on \(\phi\) and the \(\phi_ i's\) the author develops a necessary and sufficient condition for an optimal design using Fréchet derivatives. Some applications of the constrained optimality criterion are presented which include C-restricted D-criterion, multiresponse modeling problem and combination of A- and D-criteria.
scientific article; zbMATH DE number 4092599
scientific article