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Under a nonlinear regression model with univariate response an algorithm forthe generation of sequential adaptive designs is studied. At each stage, thecurrent design is augmented by adding $p$ design points where $p$ is thedimension of the parameter of the model. The augmenting $p$ points are suchthat, at the current parameter estimate, they constitute the locally D-optimaldesign within the set of all saturated designs. Two relevant subclasses ofnonlinear regression models are focused on, which were considered in previouswork of the authors on the adaptive Wynn algorithm: firstly, regression modelssatisfying the `saturated identifiability condition' and, secondly, generalizedlinear models. Adaptive least squares estimators and adaptive maximumlikelihood estimators in the algorithm are shown to be strongly consistent andasymptotically normal, under appropriate assumptions. For both model classes,if a condition of `saturated D-optimality' is satisfied, the almost sureasymptotic D-optimality of the generated design sequence is implied by thestrong consistency of the adaptive estimators employed by the algorithm. Thecondition states that there is a saturated design which is locally D-optimal atthe true parameter point (in the class of all designs).

A $p$-step-ahead sequential adaptive algorithm for D-optimal nonlinear regression design