Robust Designs For Fitting Linear

This paper considers linear models with misspeciication of the form f(x) = E(yjx) = P p j=1 j g j (x) + h(x), where h(x) is an unknown function. We assume that the true response function f comes from a reproducing kernel Hilbert space and the estimates of the parameters j are obtained by the standard least squares method. A sharp upper bound for the mean squared error is found in terms of the norm of h. This upper bound is used to choose a design that is robust against the model bias. It is shown that the continuous uniform design on the experimental region is the all-bias design. The numerical results of several examples show that all-bias designs perform well when some model bias is present for low dimensional cases.