Robust designs for fitting linear models with misspecification

This paper considers linear models with misspecification of the form f(x) = E(y\x) = Sigma(j=1)(p) theta(j)g(j)(x) + h(x), where h(x) is an unknown fu nction. We assume that the true response function f comes from a reproducin g kernel Hilbert space and the estimates of the parameters theta(j) are obt ained by the standard least squares method. A sharp upper bound for the mea n squared error is found in terms of the norm of h. This upper bound is use d to choose a design that is robust against the model bias. It is shown tha t the continuous uniform design on the experimental region is the all-bias design. The numerical results of several examples show that all-bias design s perform well when some model bias is present in low dimensional cases.