A general criterion for factorial designs under model uncertainty
A general criterion for factorial designs under model uncertainty
Motivated by two industrial experiments in which rather extreme prior knowledge was used to choose the design, we show that the QB criterion, which aims to improve the estimation in as many models as possible by incorporating experimenters’ prior knowledge along with an approximation to the As criterion, is more general and has a better statistical interpretation than many standard criteria. The generalization and application of the criterion to different types of designs are presented. The relationships between QB and other criteria for different situations are explored. It is shown that the E(s2) criterion is a special case of QB and several aberration-type criteria are limiting cases of our criterion, so that QB provides a bridge between alphabetic optimality and aberration. The two case studies illustrate the potential benefits of the QB criterion. R programs for calculating QB are available online as supplemental materials.
231-242
Tsai, Pi-Wen
752a8e50-aabf-4f40-bb8a-1313d2c60edf
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03
1 May 2010
Tsai, Pi-Wen
752a8e50-aabf-4f40-bb8a-1313d2c60edf
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03
Tsai, Pi-Wen and Gilmour, Steven G.
(2010)
A general criterion for factorial designs under model uncertainty.
Technometrics, 52 (2), .
(doi:10.1198/TECH.2010.08093).
Abstract
Motivated by two industrial experiments in which rather extreme prior knowledge was used to choose the design, we show that the QB criterion, which aims to improve the estimation in as many models as possible by incorporating experimenters’ prior knowledge along with an approximation to the As criterion, is more general and has a better statistical interpretation than many standard criteria. The generalization and application of the criterion to different types of designs are presented. The relationships between QB and other criteria for different situations are explored. It is shown that the E(s2) criterion is a special case of QB and several aberration-type criteria are limiting cases of our criterion, so that QB provides a bridge between alphabetic optimality and aberration. The two case studies illustrate the potential benefits of the QB criterion. R programs for calculating QB are available online as supplemental materials.
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Published date: 1 May 2010
Organisations:
Statistics
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Local EPrints ID: 174525
URI: http://eprints.soton.ac.uk/id/eprint/174525
ISSN: 0040-1706
PURE UUID: 0eed0778-a296-46e4-9c0f-31a946741971
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Date deposited: 14 Feb 2011 16:11
Last modified: 14 Mar 2024 02:34
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Author:
Pi-Wen Tsai
Author:
Steven G. Gilmour
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