Optimal Design for a Weighted Set of Estimable Functions

• Activity Number: 298
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Jonathan W. Stallings*+ and John P. Morgan
• Companies: North Carolina State University and Virginia Tech
• Keywords: Optimal design ; Weighted optimality ; A-criterion ; Baseline parameterization ; Weighted variances

Abstract

Standard design criteria like the A-, E-, and D-criterion implicitly assume the experimenter is equally interested in all estimable functions. However, these criteria are poor assessments of a design when the goals of an experiment imply differential interest. To reflect relative importance, weights are assigned to variances so that greater weight implies greater interest. Motivated by standard variance-based criteria, this talk introduces a flexible class of design measures based on these weighted variances, leading to designs tailored to efficient estimation of those functions with larger weight. A specific weighted criterion is shown to evaluate designs with respect to their ability to estimate a large number of estimable functions with any set of chosen weights. Finally, this framework is used to find optimal plans for a baseline-parameterized model detailed in Mukerjee and Tang (Biometrika 99, 2012, 71-84).