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Alexander duality in experimental designs

Maruri-Aguilar, Hugo, Saenz-de-Cabezon, Eduardo and Wynn, Henry P. (2013) Alexander duality in experimental designs. Annals of the Institute of Statistical Mathematics, 65 (4). pp. 667-686. ISSN 0020-3157

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Abstract

If F is a full factorial design and D is a fraction of F, then for a given monomial ordering, the algebraic method gives a saturated polynomial basis for D which can be used for regression. Consider now an algebraic basis for the complementary fraction of D in F, built under the same monomial ordering. We show that the basis for the complementary fraction is the Alexander dual of the first basis, constructed by shifting monomial exponents. For designs with two levels, the Alexander dual uses the traditional definition for simplicial complexes, while for designs with more than two levels, the dual is constructed with respect to the basis for the design F. This yields various new constructions for designs, where the basis and linear aberration can easily be read from the duality.

Item Type: Article
Official URL: http://www.ism.ac.jp/editsec/aism/index.html
Additional Information: © 2012 The Institute of Statistical Mathematics, Tokyo
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Decision Support and Risk Group (DSRG)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Funders: Engineering and Physical Sciences Research Council, Ministerio de Ciencia e Innovación of Spain
Projects: EP/D048893/1, MTM2009-13842-C02-01
Date Deposited: 21 Aug 2013 07:30
URL: http://eprints.lse.ac.uk/51793/

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