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Alexander duality in experimental designs

Author

Listed:
  • Hugo Maruri-Aguilar
  • Eduardo Sáenz-de-Cabezón
  • Henry Wynn

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. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Hugo Maruri-Aguilar & Eduardo Sáenz-de-Cabezón & Henry Wynn, 2013. "Alexander duality in experimental designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 667-686, August.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:4:p:667-686
    DOI: 10.1007/s10463-012-0390-9
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    References listed on IDEAS

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    1. Yael Berstein & Hugo Maruri-Aguilar & Shmuel Onn & Eva Riccomagno & Henry Wynn, 2010. "Minimal average degree aberration and the state polytope for experimental designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 673-698, August.
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