A1107
Title: A maximin $\Phi_{p}$-efficient design for multivariate generalized linear models
Authors: Yiou Li - DePaul University (United States) [presenting]
Abstract: Experimental designs for a generalized linear model (GLM) often depend on the model's specification, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with the uncertainties of these model specifications, it is important to construct optimal designs with high efficiency under such uncertainties. Existing methods, such as Bayesian experimental designs, often use prior distributions of model specifications to incorporate model uncertainties into the design criterion. Alternatively, one can obtain the design by optimizing the worst-case design efficiency with respect to the uncertainties of model specifications. A new Maximin $\Phi_p$-Efficient (or Mm-$\Phi_p$ for short) design is proposed, aiming to maximize the minimum $Phi_p$-efficiency under model uncertainties. Based on the theoretical properties of the proposed criterion, an efficient algorithm with sound convergence properties is developed to construct the Mm-$\Phi_p$ design. The performance of the proposed Mm-$\Phi_p$ design is assessed through several numerical examples.
