On the regularization of singular c-optimal designs

We consider the design of c-optimal experiments for the estimation of a scalar function h(θ) of the parameters θ in a nonlinear regression model. A c-optimal design ξ∗ may be singular, and we derive conditions ensuring the asymptotic normality of the Least-Squares estimator of h(θ) for a singular design over a finite space. As illustrated by an example, the singular designs for which asymptotic normality holds typically depend on the unknown true value of θ, which makes singular c-optimal designs of no practical use in nonlinear situations. Some simple alternatives are then suggested for constructing nonsingular designs that approach a c-optimal design under some conditions.