Minimax designs for approximately linear regression

Abstract We consider the approximately linear regression model E[y|x] = z T (x)θ + ƒ(x), x∈ S , where ƒ(x) is a non-linear disturbance restricted only by a bound on its L 2(S) norm, and where S is the design space. For loss functions which are monotonic functions of the mean squared error matrix, we derive a theory to guide in the construction of designs which minimize the maximum (over ƒ ;) loss. We then specialize to the case zT (x) = (1, xT), so that the fitted surface is a plane. In this case we give minimax designs for loss functions corresponding to the classical D-, A-, E-, Q- and G-optimality criteria.

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