A criterion for model-robust design of experiments

The paper considers the design of experiments for linear models with misspecification, of the form t(x) = Sigma
_{i = 1}

^p
thetas
_i
Phi
_i
(x) + r(x), where r(x) is an unknown deviation from the regression model. Considering a modeling of this misspecification, the goal is to obtain robust designs which minimize the integral quadratic risk. A kernel-based representation (Gaussian process) is chosen to model the misspecification and a new criterion is derived, composed of the classical L-criterion, plus a specific term. Robust designs are then given for polynomial regression, in the particular case of a Gaussian kernel for the Gaussian process. The benefits of this approach are finally demonstrated through comparison of the performance (in terms of integral quadratic error) of such designs versus L-optimal and uniform designs on a simple illustrative example