Optimal design for multivariate multiple linear regression with set-identified response

Abstract

We consider the partially identified regression model with set-identified responses, where the estimator is the set of the least square estimators obtained for all possible choices of points sampled from set-identified observations. We address the issue of determining the optimal design for this case and show that, for objective functions mimicking those for several classical optimal designs, their set-identified analogues coincide with the optimal designs for point-identified real-valued responses.