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Article: D-optimal axial designs for quadratic and cubic additive mixture models

TitleD-optimal axial designs for quadratic and cubic additive mixture models
Authors
KeywordsAdditive mixture model
Axial design
D-optimality
Uniformity of designs
Issue Date1998
PublisherBlackwell Publishing Asia. The Journal's web site is located at http://www.blackwellpublishing.com/journals/ANZS
Citation
Australian And New Zealand Journal Of Statistics, 1998, v. 40 n. 3, p. 359-371 How to Cite?
AbstractThe paper discusses D-optimal axial designs for the additive quadratic and cubic mixture models Σ 1≤i≤q(β ix i + β iix i 2) and Σ 1≤i≤q(β ix i + β iix i 2 + β iiix i 3), where x i ≥ 0, x 1 + ⋯ + x q = 1. For the quadratic model, a saturated symmetric axial design is used, in which support points are of the form (x 1, ⋯ , x q) = [1 -(q - 1)δ i, δ i, ⋯ , δ i], where i = 1, 2 and 0 ≤ δ 2 < δ 1 ≤ 1/(q - 1). It is proved that when 3 ≤ q ≤ 6, the above design is D-optimal if δ 2 = 0 and & δ 1 = 1/(q - 1), and when q ≥ 7 it is D-optimal if δ 2 = 0 and δ 1 = [5q - 1 - (9q 2 - 10q + 1) 1/2]/(4q 2). Similar results exist for the cubic model, with support points of the form (x 1,⋯, x q) = [1 - (q - 1)δ i, δ i,⋯, δ i], where i. = 1, 2, 3 and 0 = δ 3 < δ 2 < δ 1 ≤ 1/(q -1). The saturated D-optimal axial design and D-optimal design for the quadratic model are compared in terms of their efficiency and uniformity. © Australian Statistical Publishing Association Inc. 1998. Published by Blackwell Publishers Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/74507
ISSN
2015 Impact Factor: 0.431
2015 SCImago Journal Rankings: 0.275
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChan, LYen_HK
dc.contributor.authorMeng, JHen_HK
dc.contributor.authorJiang, YCen_HK
dc.contributor.authorGuan, YNen_HK
dc.date.accessioned2010-09-06T07:02:00Z-
dc.date.available2010-09-06T07:02:00Z-
dc.date.issued1998en_HK
dc.identifier.citationAustralian And New Zealand Journal Of Statistics, 1998, v. 40 n. 3, p. 359-371en_HK
dc.identifier.issn1369-1473en_HK
dc.identifier.urihttp://hdl.handle.net/10722/74507-
dc.description.abstractThe paper discusses D-optimal axial designs for the additive quadratic and cubic mixture models Σ 1≤i≤q(β ix i + β iix i 2) and Σ 1≤i≤q(β ix i + β iix i 2 + β iiix i 3), where x i ≥ 0, x 1 + ⋯ + x q = 1. For the quadratic model, a saturated symmetric axial design is used, in which support points are of the form (x 1, ⋯ , x q) = [1 -(q - 1)δ i, δ i, ⋯ , δ i], where i = 1, 2 and 0 ≤ δ 2 < δ 1 ≤ 1/(q - 1). It is proved that when 3 ≤ q ≤ 6, the above design is D-optimal if δ 2 = 0 and & δ 1 = 1/(q - 1), and when q ≥ 7 it is D-optimal if δ 2 = 0 and δ 1 = [5q - 1 - (9q 2 - 10q + 1) 1/2]/(4q 2). Similar results exist for the cubic model, with support points of the form (x 1,⋯, x q) = [1 - (q - 1)δ i, δ i,⋯, δ i], where i. = 1, 2, 3 and 0 = δ 3 < δ 2 < δ 1 ≤ 1/(q -1). The saturated D-optimal axial design and D-optimal design for the quadratic model are compared in terms of their efficiency and uniformity. © Australian Statistical Publishing Association Inc. 1998. Published by Blackwell Publishers Ltd.en_HK
dc.languageengen_HK
dc.publisherBlackwell Publishing Asia. The Journal's web site is located at http://www.blackwellpublishing.com/journals/ANZSen_HK
dc.relation.ispartofAustralian and New Zealand Journal of Statisticsen_HK
dc.subjectAdditive mixture modelen_HK
dc.subjectAxial designen_HK
dc.subjectD-optimalityen_HK
dc.subjectUniformity of designsen_HK
dc.titleD-optimal axial designs for quadratic and cubic additive mixture modelsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1369-1473&volume=40&issue=3&spage=901&epage=913&date=1998&atitle=D-optimal+axial+designs+for+quadratic+and+cubic+additive+mixtures+modelen_HK
dc.identifier.emailChan, LY: plychan@hku.hken_HK
dc.identifier.authorityChan, LY=rp00093en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1111/1467-842X.00039-
dc.identifier.scopuseid_2-s2.0-0042063374en_HK
dc.identifier.hkuros46720en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0042063374&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume40en_HK
dc.identifier.issue3en_HK
dc.identifier.spage359en_HK
dc.identifier.epage371en_HK
dc.identifier.isiWOS:000075782100010-
dc.publisher.placeAustraliaen_HK
dc.identifier.scopusauthoridChan, LY=7403540482en_HK
dc.identifier.scopusauthoridMeng, JH=8394597400en_HK
dc.identifier.scopusauthoridJiang, YC=55496934500en_HK
dc.identifier.scopusauthoridGuan, YN=7202924075en_HK

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