Convergent Design Sequences, for Sufficiently Regular Optimality Criteria, II: Singular Case

Atwood, Corwin L.

Ann. Statist., Tome 8 (1980) no. 1, p. 894-912 / Harvested from Project Euclid

Résumé

Let an optimality criterion $\Phi$ satisfy regularity conditions, including convexity and possession of two continuous derivatives at nonsingular $\mathbf{M}$. $\Phi\{\mathbf{M})$ may be minimized at a singular $\mathbf{M}$. A class of design sequences $\{\xi_n\}$ is shown to make $\Phi\lbrack \mathbf{M}(\xi_n) \rbrack$ converge monotonically to the minimum value. An equivalence theorem for $\Phi$-optimality follows. Techniques which are applicable include vertex direction, conjugate gradient projection, quadratic and "diagonalized quadratic" methods for changing the design weights, and gradient-based methods for making small changes in the support points. Methods are also considered which approximate $\Phi$ by a criterion which is infinite for singular $\mathbf{M}$. The results are applied to an example with $D_s$-optimality.

Détail

Publié le : 1980-07-14
Classification:  Singular optimal experimental designs,  $D_s$-optimality,  $L$-optimality,  $\Phi$-optimality,  iterative design optimization,  equivalence theorem for optimal designs,  62K05,  65B99