Under a nonlinear regression model with univariate response an algorithm for the generation of sequential adaptive designs is studied. At each stage, the current design is augmented by adding $p$ design points where $p$ is the dimension of the parameter of the model. The augmenting $p$ points are such that, at the current parameter estimate, they constitute the locally D-optimal design within the set of all saturated designs. Two relevant subclasses of nonlinear regression models are focused on, which were considered in previous work of the authors on the adaptive Wynn algorithm: firstly, regression models satisfying the `saturated identifiability condition' and, secondly, generalized linear models. Adaptive least squares estimators and adaptive maximum likelihood estimators in the algorithm are shown to be strongly consistent and asymptotically normal, under appropriate assumptions. For both model classes, if a condition of `saturated D-optimality' is satisfied, the almost sure asymptotic D-optimality of the generated design sequence is implied by the strong consistency of the adaptive estimators employed by the algorithm. The condition states that there is a saturated design which is locally D-optimal at the true parameter point (in the class of all designs).

翻译：研究了一种在单变量响应非线性回归模型下生成序贯自适应设计的算法。在每一步中，当前设计通过添加$p$个设计点进行增广，其中$p$是模型参数的维度。增广的$p$个点使得在当前参数估计下，它们构成所有饱和设计集合中的局部D-最优设计。重点关注了两类相关的非线性回归模型子类，这些子类在作者先前关于自适应Wynn算法的工作中已得到考虑：其一为满足“饱和可辨识条件”的回归模型，其二为广义线性模型。在适当假设下，算法中的自适应最小二乘估计量和自适应极大似然估计量被证明具有强相合性和渐近正态性。对于这两类模型，若满足“饱和D-最优性”条件，则算法所生成的设计序列几乎必然渐近D-最优，这一结论由算法中使用的自适应估计量的强相合性所推导。该条件指出：存在一个饱和设计，其在真实参数点（在所有设计构成的集合中）是局部D-最优的。