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Optimal designs for multivariable spline models

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
M09/16
University of Southampton, Southampton Statistical Sciences Research Institute
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
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. University of Southampton, Southampton Statistical Sciences Research Institute 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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Published date: 30 September 2009

Identifiers

Local EPrints ID: 69157
URI: https://eprints.soton.ac.uk/id/eprint/69157
PURE UUID: 50f63312-b91c-4829-90f4-76ef51e33cfe
ORCID for Stefanie Biedermann: ORCID iD orcid.org/0000-0001-8900-8268
ORCID for David C. Woods: ORCID iD orcid.org/0000-0001-7648-429X

Catalogue record

Date deposited: 22 Oct 2009
Last modified: 27 Jul 2019 00:34

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