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In multi-response regression models, the error covariance matrix is neverknown in practice. Thus, there is a need for optimal designs which are robustagainst possible misspecification of the error covariance matrix. In thispaper, we approximate the error covariance matrix with a neighbourhood ofcovariance matrices, in order to define minimax D-optimal designs which arerobust against small departures from an assumed error covariance matrix. It iswell known that the optimization problems associated with robust designs arenon-convex, which makes it challenging to construct robust designs analyticallyor numerically, even for one-response regression models. We show that theobjective function for the minimax D-optimal design is a difference of twoconvex functions. This leads us to develop a flexible algorithm for computingminimax D-optimal designs, which can be applied to any multi-response modelwith a discrete design space. We also derive several theoretical results forminimax D-optimal designs, including scale invariance and reflection symmetry.

Minimax D-optimal designs for multivariate regression models with multi-factors