A class of model-robust optimal designs, based on an extension of the standard optimality criteria to cases where there exist some prior information on the validity of a response function, is considered. Under this set-up, the concept of the "model validity range" is introduced and explored. A necessary condition for optimality is obtained for the determinant criterion (D-optimality in the classical case). A modified version of this criterion is proposed and discussed. The corresponding results provide upper and low bounds for the original problem and help to construct approximate solutions, when contamination is relatively small. Optimal designs for simple but commonly used regression models are obtained and studied.
Bibliographical noteFunding Information:
The authors are thankful to the referees and the associate editor for their suggestions, which significantly improved the presentation of this paper. Valery Fedorov’s research was supported by the Applied Mathematical Sciences Research Program, Office of Energy Research, U.S. Department of Energy under contract DE-AC05-84OR21400 with Lockheed Martin Energy Systems, Inc.
- First-order iterative algorithm
- Linear regression
- Mean squared error
- Model validity* D -optimality
- Model-robust design