Abstract: Adaptive designs that optimize the Fisher information associated with a nonlinear experiment are considered. Asymptotic properties of the maximum likelihood estimate and related statistical inference based on dependent data generated by sequentially designed adaptive nonlinear experiments are explored. Conditions on the experimental designs that ensure first order efficiency of the maximum likelihood estimate when the parametrization of the nonlinear model is sufficiently smooth and regular are derived. A few interesting open questions that arise naturally in course of the investigation are mentioned and briefly discussed.
Key words and phrases: Adaptive sequential designs, first order efficiency, Fisher information, local Φ-optimality, martingales, maximum likelihood, nonlinear models.