Optimal designs for quantile regression models

Abstract

Despite of their importance optimal designs for quantile regression models have not been developed so far. In this paper we investigate the D-optimal design problem for the location scale nonlinear quantile regression model. We provide a necessary condition to check for the optimality of a given design and use it to determine bounds for the number of support points of locally D-optimal designs. The results are illustrated determining locally, Bayesian and standardized maximin D-optimal designs for quantile regression analysis in the Michaelis-Menten and EMAX model, where the location and the scale function are related by a known link function.