A comparison between the Gröbner bases approach and hidden projection properties in factorial designs

Evangelaras, H; Koukouvinos, C

dc.contributor.author	Evangelaras, H	en
dc.contributor.author	Koukouvinos, C	en
dc.date.accessioned	2014-03-01T01:23:23Z
dc.date.available	2014-03-01T01:23:23Z
dc.date.issued	2006	en
dc.identifier.issn	0167-9473	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16936
dc.subject	D- and Ds-efficiency	en
dc.subject	Estimable effects	en
dc.subject	Gröbner bases	en
dc.subject	Hidden projection	en
dc.subject	Leading terms	en
dc.subject	Plackett-Burman designs	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Statistics & Probability	en
dc.subject.other	Data recording	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Problem solving	en
dc.subject.other	Statistical methods	en
dc.subject.other	D- and D-efficiency	en
dc.subject.other	Gröbner bases	en
dc.subject.other	Hidden projection	en
dc.subject.other	Leading terms	en
dc.subject.other	Plackett-Burman designs	en
dc.subject.other	Computational methods	en
dc.title	A comparison between the Gröbner bases approach and hidden projection properties in factorial designs	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.csda.2003.11.022	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.csda.2003.11.022	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	Screening designs are useful for situations where a large number of factors (q) are examined but only few (k) of these are expected to be important. Plackett-Burman designs have traditionally been studied for this purpose. Since these designs are only main effects plans and since the number of runs are greater than the number of active factors (main effects), there are plenty of degrees of freedom unused for identifying and estimating interactions of factors. Computational Algebraic Geometry can be used to solve identifiability problems in design of experiments in Statistics. The theory of Grobner bases allows one to identify the whole set of estimable effects (main or interactions) of the factors of the design. On the other hand, the hidden projection property approach, that deals with the same identification problem, provides a measure of how efficient the identification of effects is. The advantages and disadvantages of both methods are discussed with application to a certain two level (fractional) factorial designs that arise from Plackett-Burman designs. (c) 2003 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Computational Statistics and Data Analysis	en
dc.identifier.doi	10.1016/j.csda.2003.11.022	en
dc.identifier.isi	ISI:000232093200006	en
dc.identifier.volume	50	en
dc.identifier.issue	1 SPEC. ISS.	en
dc.identifier.spage	77	en
dc.identifier.epage	88	en