Abstract
For a regular optimality criterion function ΦΦ, a sequence of design measures {ξn}{ξn} is generated using the iteration ξn+1=(1−αn)ξn+αnξnξn+1=(1−αn)ξn+αnξn, where ξnξn is chosen to minimize ∇Φ(M(ξn),M(ξ))∇Φ(M(ξn),M(ξ)) over all ξξ and {αn}{αn} is a prescribed sequence of numbers from (0, 1). This is called a general step-length algorithm for ΦΦ. Typical conditions on {αn}{αn} are αn→0αn→0 and Σnαn=∞Σnαn=∞. In this paper, a dichotomous behavior of {ξn}{ξn} is proved under the above conditions on {αn}{αn} for ΦΦ satisfying some mild regularity conditions. Sufficient conditions for convergence to optimal designs are also established. This can be applied to show that the {ξn}{ξn} as constructed above do converge to an optimal design for most of the trace-related and determinant-related design criteria.
Citation
Chien-Fu Wu. Henry P. Wynn. "The Convergence of General Step-Length Algorithms for Regular Optimum Design Criteria." Ann. Statist. 6 (6) 1273 - 1285, November, 1978. https://doi.org/10.1214/aos/1176344373
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