Minimax designs for approximately linear regression
نویسنده
چکیده
We consider the approximately linear regression model E b 1x1 = I(x) 0 + f(x), XE S, where f(x) is a non-linear disturbance restricted only by a bound on its &(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 f) loss. We then specialize to the case zT(.r) = (I,x~), 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-, Qand G-optimality criteria. AMS Subject ClassiJication: Primary 62K05; secondary 62F35, 62505.
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