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

Li, Qiyu; Molchanov, Ilya (2019). Optimal design for multivariate multiple linear regression with set-identified response. Journal of statistical planning and inference, 203, pp. 215-223. Elsevier 10.1016/j.jspi.2019.04.003

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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.

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