Abstract: Experimental designs for generalized linear models often depend on the specification of the model, including the link function, 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 the model specifications. In this work, we propose a new Maximin Φ_p-Efficient (or Mm-Φ_p for short) design that aims to maximize the minimum Φp-efficiency under model uncertainties. Based on the theoretical properties of the proposed criterion, we develop an efficient algorithm with sound convergence properties to construct the Mm-Φ_p design. The performance of the proposed Mm-Φ_p design is assessed using several numerical examples.

Key words and phrases: Φ_p-criterion, dsesign efficiency, efficient algorithm, model uncertainty, optimal design.