论文标题
当丢失数据随机发生时，可强大的最佳设计
Robust Optimal Designs when Missing Data Happen at Random
论文作者
论文摘要
在本文中，我们研究了仅指定拟合回归模型时预测响应的强大最佳设计问题，并且可能完全随机缺少观测值。直观的想法如下：我们假设数据是随机丢失的，并且应用了完整的案例分析。为了说明丢失数据的出现，我们选择的设计标准是，对于丢失的指标，平均（在设计空间）的平均平方误差的平均值。 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.最大化的MMPE是拟合回归模型附近的``最坏''损失。最小化设计类别的最大MMPE，我们获得了强大的``minimax''设计。构建的强大设计可提供保护，以防止因模型误差而导致的预测错误增加。
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.
