D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix. For non-linear models, the Fisher information matrix depends on the unknown parameter vector of interest, leading to a weird situation that in order to obtain the D-optimal design, one needs to have knowledge of the parameter to be estimated. One solution to this problem is to choose the design points sequentially, optimizing the D-optimality criterion using parameter estimates based on available data, followed by updating the parameter estimates using maximum likelihood estimation. On the other hand, there are many non-linear models for which closed-form results for D-optimal designs are available, but because such solutions involve the parameters to be estimated, they can only be used by substituting "guestimates" of parameters. In this paper, a hybrid sequential strategy called PICS (Plug into closed-form solution) is proposed that replaces the optimization of the objective function at every single step by a draw from the probability distribution induced by the known optimal design by plugging in the current estimates. Under regularity conditions, asymptotic normality of the sequence of estimators generated by this approach are established. Usefulness of this approach in terms of saving computational time and achieving greater efficiency of estimation compared to the standard sequential approach are demonstrated with simulations conducted from two different sets of models.

翻译：用于估计响应模型参数的D最优设计通过最大化费舍尔信息矩阵的行列式推导得出。对于非线性模型，费舍尔信息矩阵依赖于未知的待估参数向量，这导致了一个奇特现象：为获得D最优设计，需要事先知晓待估计的参数。该问题的一种解决方案是序贯选择设计点：基于已有数据通过参数估计值优化D最优准则，随后通过极大似然估计更新参数估计值。另一方面，许多非线性模型存在D最优设计的闭式解，但由于这类解涉及待估参数，只能通过代入参数的"猜测估计值"来使用。本文提出了一种名为PICS（代入闭式解）的混合序贯策略，该方法通过代入当前估计值，从已知最优设计诱导的概率分布中抽样，取代每一步的目标函数优化过程。在正则性条件下，证明了该方法生成的估计量序列具有渐近正态性。通过对两组不同模型的仿真实验，展示了该方法在节省计算时间、提升估计效率方面相较于标准序贯方法的优越性。