2019/10/02 by Lucy L. Gao, Gao, Lucy L., Julie Zhou +1
Computer Science · Decision Sciences · Engineering · #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Manufacturing Process and Optimization #Methodology (stat.ME) #Optimal Experimental Design Methods
paper · pdf · doi:10.48550/arxiv.1910.00745
openalex publication_date 2019/10/02 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28
In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we approximate the error covariance matrix with a neighbourhood of covariance matrices, in order to define minimax D-optimal designs which are robust against small departures from an assumed error covariance matrix. It is well known that the optimization problems associated with robust designs are non-convex, which makes it challenging to construct robust designs analytically or numerically, even for one-response regression models. We show that the objective function for the minimax D-optimal design is a difference of two convex functions. This leads us to develop a flexible algorithm for computing minimax D-optimal designs, which can be applied to any multi-response model with a discrete design space. We also derive several theoretical results for minimax D-optimal designs, including scale invariance and reflection symmetry.