Statistica Sinica

Rong-Xian Yue
and Fred J. Hickernell

Abstract:This paper considers linear models with misspecification of the form , where is an unknown function. We assume that the true response function comes from a reproducing kernel Hilbert space and the estimates of the parameters 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 . 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 in low dimensional cases.

Key words and phrases:Linear models with misspecification, model-robust designs, reproducing kernel Hilbert spaces.