Optimal Designs for Quantile Regression Models

Despite their importance, optimal designs for quantile regression models have not been developed so far. In this article, we investigate the <italic>D</italic>-optimal design problem for nonlinear quantile regression analysis. We provide a necessary condition to check the optimality of a given design and use it to determine bounds for the number of support points of locally <italic>D</italic>-optimal designs. The results are illustrated, determining locally, Bayesian and standardized maximin <italic>D</italic>-optimal designs for quantile regression analysis in the Michaelis--Menten and EMAX model, which are widely used in such important fields as toxicology, pharmacokinetics, and dose--response modeling.