Optimal design for smooth supersaturated models

Smooth supersaturated models are interpolation models in which the underlying model size, and typically the degree, is higher than would normally be used in statistics, but where the extra degrees of freedom are used to make the model smooth using a standard second derivative measure of smoothness. Here, the solution is derived from a closed-form quadratic programme, leading to tractable matrix representations. This representation aids considerably in the choice of optimal knots in the interpolation case and in the optimal design when the SSM is used as a way of obtaining kernels, but where the statistical problem is set up separately. Some examples are given in one and two dimensions.