Optimal designs for multivariable spline models

Abstract

In this paper, we investigate optimal designs for multivariate additive spline regression models. We assume that the knot locations are unknown, so must be estimated from the data. In this situation, the Fisher information for the full parameter vector depends on the unknown knot locations, resulting in a non-linear design problem. We show that locally, Bayesian and maximin D-optimal designs can be found as the products of the optimal designs in one dimension. A similar result is proven for Q-optimality in the class of all product designs.