Biedermann, Stefanie, Dette, Holger and Woods, David C.
Optimal designs for multivariable spline models. Southampton, UK, University of Southampton, Southampton Statistical Sciences Research Institute, 28pp.
(S3RI Methodology Working Papers, M09/16).
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
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