Title: Designing to estimate parameters independently of each other
Authors: Saumen Mandal - University of Manitoba (Canada) [presenting]
Ben Torsney - University of Glasgow (United Kingdom)
Mohammad Chowdhury - University of Calgary (Canada)
Abstract: An optimal design problem is considered where the criterion function is neither convex nor concave. Determining optimality conditions for such criteria is quite challenging. Motivated by this fact, we first establish two sets of optimality conditions for a non-concave criterion using Lagrangian theory and directional derivatives. We then apply these conditions to construct optimal designs for some regression models in which it is desired to estimate certain parameters as independently of each other as possible. We minimize absolute covariances among the least-squares estimators of the parameters in a linear model, thereby rendering the parameter estimators approximately uncorrelated with each other. We then consider the problem of obtaining more than two parameter estimators with more than one zero correlation among them. We achieve this goal by creating a compound criterion and then solving the problem by employing a simultaneous optimization technique. More specifically, we transform the problem to an optimization problem in which we maximize a number of functions of the design weights simultaneously. The methodologies are formulated for a general regression model and are explored through some examples, including one practical problem arising in chemistry.