Optimal designs based on exact confidence regions for parameter estimation of a nonlinear regression model

This paper is concerned with the proposal of optimality criteria, referred to as X  - and X^′$X^{\prime }$-optimality criteria, and the construction of X  - and X^′$X^{\prime }$-optimal designs, for nonlinear regression models. These optimal designs aim at improving the estimation of parameters of this class of models. The principle of these criteria is the minimization, with respect to the design, of the expected volume of a particular exact parametric confidence region. In this paper we give detailed definitions, properties, and computation methods of X  - and X^′$X^{\prime }$-optimal designs. We also compare these designs with the classic local D-optimal designs, with regard to robustness and efficiency, for two very well-known academic models (Box–Lucas and Michaelis–Menten models).