Alexander duality in experimental designs

  1. Maruri-Aguilar, H. 3
  2. Sáenz-De-Cabezón, E. 1
  3. Wynn, H.P. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 London School of Economics and Political Science
    info

    London School of Economics and Political Science

    Londres, Reino Unido

    ROR https://ror.org/0090zs177

  3. 3 University of London
    info

    University of London

    Londres, Reino Unido

    ROR https://ror.org/04cw6st05

Revista:
Annals of the Institute of Statistical Mathematics

ISSN: 0020-3157

Año de publicación: 2013

Volumen: 65

Número: 4

Páginas: 667-686

Tipo: Artículo

DOI: 10.1007/S10463-012-0390-9 SCOPUS: 2-s2.0-84881156222 WoS: WOS:000322386500003 GOOGLE SCHOLAR

Otras publicaciones en: Annals of the Institute of Statistical Mathematics

Resumen

If {Mathematical expression} is a full factorial design and {Mathematical expression} is a fraction of {Mathematical expression}, then for a given monomial ordering, the algebraic method gives a saturated polynomial basis for {Mathematical expression} which can be used for regression. Consider now an algebraic basis for the complementary fraction of {Mathematical expression} in {Mathematical expression}, 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 {Mathematical expression}. This yields various new constructions for designs, where the basis and linear aberration can easily be read from the duality. © 2012 The Institute of Statistical Mathematics, Tokyo.