Optimal design for additive partially nonlinear models
Optimal design for additive partially nonlinear models
We develop optimal design theory for additive partially nonlinear regression models, showing that Bayesian and standardized maximin D-optimal designs can be found as the products of the corresponding optimal designs in one dimension. A sufficient condition under which analogous results hold for Ds-optimality is derived to accommodate situations in which only a subset of the model parameters is of interest. To facilitate prediction of the response at unobserved locations, we prove similar results for Q-optimality in the class of all product designs. The usefulness of this approach is demonstrated through an application from the automotive industry, where optimal designs for least squares regression splines are determined and compared with designs commonly used in practice.
additive model, bayesian d-optimality, partially nonlinear model, product design, q-optimality, standardised maximin d-optimality
449-458
Biedermann, S.
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, H.
6a1faa1a-fab9-43e1-ab2b-d2f0a5430750
Woods, D.C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
June 2011
Biedermann, S.
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, H.
6a1faa1a-fab9-43e1-ab2b-d2f0a5430750
Woods, D.C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Biedermann, S., Dette, H. and Woods, D.C.
(2011)
Optimal design for additive partially nonlinear models.
Biometrika, 98 (2), .
(doi:10.1093/biomet/asr001).
Abstract
We develop optimal design theory for additive partially nonlinear regression models, showing that Bayesian and standardized maximin D-optimal designs can be found as the products of the corresponding optimal designs in one dimension. A sufficient condition under which analogous results hold for Ds-optimality is derived to accommodate situations in which only a subset of the model parameters is of interest. To facilitate prediction of the response at unobserved locations, we prove similar results for Q-optimality in the class of all product designs. The usefulness of this approach is demonstrated through an application from the automotive industry, where optimal designs for least squares regression splines are determined and compared with designs commonly used in practice.
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Published date: June 2011
Keywords:
additive model, bayesian d-optimality, partially nonlinear model, product design, q-optimality, standardised maximin d-optimality
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Statistics
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Local EPrints ID: 144481
URI: http://eprints.soton.ac.uk/id/eprint/144481
ISSN: 0006-3444
PURE UUID: 6530d9d4-2406-46f5-9411-f46c783aae38
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Date deposited: 14 Apr 2010 14:49
Last modified: 14 Mar 2024 02:51
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Author:
H. Dette
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