A geometric characterization of c-optimal designs for heteroscedastic regression

Abstract

We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23.