Techniques for the Construction of Robust Regression Designs

• Activity Number: 698
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Maryam Daemi*+ and Douglas P. Wiens
• Companies: University of Alberta and University of Alberta
• Keywords: Alphabetic optimality ; Bias ; Minimax ; Invariance ; Approximate straight line regression

Abstract

The authors review and extend the literature on robust regression designs. Even for straight line regression, there are cases in which the optimally robust designs - in a minimax mean squared error sense, with the maximum evaluated as the 'true' model varies over a neighbourhood of that fitted by the experimenter - have not yet been constructed. They point out a gap within the part of the minimax method related to minimizing the maximized loss function based on A- and E-optimality criteria: it is not applicable to finding an optimal design for these criteria when the emphasis is much more on the errors from bias than on those from variation. They fill this gap in the literature, and in so doing introduce a method of construction that is conceptually and mathematically simpler than the sole competing method. The technique used injects additional insight into the structure of the solutions. In the cases that the optimality criteria employed result in designs that are not invariant under changes in the design space, their methods also allow for an investigation of the resulting changes in the designs.