In this article, we investigate the robust optimal design problem for the prediction of response when the fitted regression models are only approximately specified, and observations might be missing completely at random. The intuitive idea is as follows: We assume that data are missing at random, and the complete case analysis is applied. To account for the occurrence of missing data, the design criterion we choose is the mean, for the missing indicator, of the averaged (over the design space) mean squared errors of the predictions. To describe the uncertainty in the specification of the real underlying model, we impose a neighborhood structure on the deterministic part of the regression response and maximize, analytically, the \textbf{M}ean of the averaged \textbf{M}ean squared \textbf{P}rediction \textbf{E}rrors (MMPE), over the entire neighborhood. The maximized MMPE is the ``worst'' loss in the neighborhood of the fitted regression model. Minimizing the maximum MMPE over the class of designs, we obtain robust ``minimax'' designs. The robust designs constructed afford protection from increases in prediction errors resulting from model misspecifications.

翻译：在本篇文章中,我们调查了在安装的回归模型仅大致指定时预测响应的稳妥最佳设计问题,而观测可能完全随机缺失。 直观想法如下: 我们假设数据随机丢失, 并应用完整的案例分析。 为了计算缺失数据的发生情况, 我们选择的设计标准是平均( 超过设计空间) 表示预测的平方差的平均值。 为了描述真实基础模型规格的不确定性, 我们为回归反应的确定性部分设置了邻里结构, 并且从分析角度将平均的\ textbf{M}Ean 的\ textbf{M}Ean 平方形 {P} { textbf{E}rrors (MMAPE) 最大化。 最优化的 MMPE 是合适的回归模型附近“worstt” 损失。 将最大 MMPE 限制在设计类别上, 我们从错误的预测中获取了稳健的精确度 。