Locally optimal designs for errors-in-variables models

Abstract

We consider the construction of optimal designs for nonlinear regression models when there are measurement errors in the covariates. Corresponding approximate design theory is developed for maximum likelihood and least-squares estimation, with the latter leading to nonconcave optimization problems. Analytical characterizations of the locally D-optimal saturated designs are provided for the Michaelis–Menten, E m a x and exponential regression models. Through concrete applications, we illustrate how measurement errors in the covariates affect the optimal choice of design and show that the locally D-optimal saturated designs are highly efficient for relatively small misspecifications of the parameter values.