Optimal designs for multivariable spline models

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Description/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