A0397
Title: Optimal robust designs with both centered and baseline factors
Authors: Xietao Zhou - KCL (United Kingdom) [presenting]
Steven Gilmour - KCL (United Kingdom)
Abstract: Traditional optimal designs are optimal under a pre-specified model. When the final fitted model differs from the pre-specified model, traditional optimal designs may cease to be optimal, and the corresponding parameter estimators may have larger variances. The $Q_B$ criterion has been proposed to offer the capacity to consider hundreds of alternative models that could potentially be useful for data from a multifactor design. The $Q_B$ criterion is extended to the scenario when eligible candidate models contain both baseline and centered parameterization factors. This shall be of interest in practice when some of the factors naturally do have a reasonable null state alongside other factors whose levels are equally important and are more naturally represented under the centered parameterization. The optimal designs are compared with their counterparts in the most recent literature and have shown that the projection capacity of eligible candidate the models/accuracy of estimation of models in terms of the $A_s$ criterion can be improved when the number of runs in the experiment is a multiple of 4 and have also examined and solved the same problem with no restrictions on the number of runs of the experiment so that it could be applied in a more general way in practice. The new version of the $Q_B$ criterion, dealing with factors under both parameterizations, is presented, followed by evaluating the robust and accurate performance of the $Q_B$ optimal designs found.
