B1899
Title: Optimal designs for minimizing some correlation-based criteria
Authors: Saumen Mandal - University of Manitoba (Canada) [presenting]
Abstract: Optimal design theory can be applied to solve a variety of optimization problems, which demand the calculation of one or more optimizing probability distributions. We consider one such problem based on some correlation-based criteria. In some regression models, it is desired to estimate certain parameters as independently of each other as possible. We construct such designs by minimizing the squared correlations between the estimators of parameters or linear combinations of the parameters of a linear model. This optimization problem is quite challenging as the criterion is neither convex nor concave. We first determine the optimality conditions for such criterion, and then construct optimal designs for some regression models. As a second problem, we construct optimal designs by minimizing the A-optimality criterion (average variance) subject to achieving zero correlation among certain parameter estimators. In this way, we can achieve two goals with one optimization problem. We achieve the goals by using the Lagrangian theory and then solving the problem by means of a simultaneous optimization technique. We consider some regression models of interest, and report the optimal designs.
