Admissibility of experimental designs in linear regression with constant term
The paper provides the mathematical and statistical details for formulating the optimality problem of designs in the linear regression setting with a constant term. In the usual notation and jargon the determination of an optimal design calls for the solution of a minimization problem, which is not an easy task. The subsets of admissible designs and invariant designs are brought into play in order to reduce the minimization effort. Specifically, the author establishes necessary conditions for admissibility whenever the regression function contains a constant term. It is further shown that the information matrix of an admissible design maximizes a linear function under certain linear restrictions. This in turn solves an unconstrained nonconstant linear optimization problem, which yields nontrivial conditions on the support points similar to the classical results of \textit{S. Karlin} and \textit{W. J. Studden} [see Ann. Math. Statistics 37, 783-815 (1966; Zbl 0151.239)]. The polynomial regression is selected as an example. For the linear setup all invariant and admissible designs are presented. In the quadratic case the support points of an invariant and admissible design are either zero or special boundary points of the experimental region.
scientific article; zbMATH DE number 4215213
scientific article