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

Robust Optimal Designs when Missing Data Happen at Random