Optimal designs for multivariable spline models
Optimal designs for multivariable spline models
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
Southampton Statistical Sciences Research Institute, University of Southampton
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
30 September 2009
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Biedermann, Stefanie, Dette, Holger and Woods, David C.
(2009)
Optimal designs for multivariable spline models
(S3RI Methodology Working Papers, M09/16)
Southampton, UK.
Southampton Statistical Sciences Research Institute, University of Southampton
28pp.
Record type:
Monograph
(Working Paper)
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
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s3ri-workingpaper-M09-16.pdf
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Published date: 30 September 2009
Identifiers
Local EPrints ID: 69157
URI: http://eprints.soton.ac.uk/id/eprint/69157
PURE UUID: 50f63312-b91c-4829-90f4-76ef51e33cfe
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Date deposited: 22 Oct 2009
Last modified: 14 Mar 2024 02:51
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Author:
Holger Dette
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