Two polynomial representations of experimental design

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Notari, Roberto; Riccomagno, Eva; Rogantin, Maria-Piera;
  • Subject: Statistics - Methodology | Statistics - Computation

In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Groebner bases and indi... View more
  • References (20)
    20 references, page 1 of 2

    Char, B., Geddes, K., Gonnet, G., Leong, B., Monogan, M., Watt, S., 1991. MAPLE V Library Reference Manual. Springer-Verlag, New York.

    Cheng, S.-W., Ye, K. Q., 2004. Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. The Annals of Statistics 32 (5), 2168-2185.

    CoCoATeam, 2005. CoCoA: a system for doing

    Draper, N. R., Pukelsheim, F., 1998. Mixture models based on homogeneous polynomials. J. Statist. Plann. Inference 71 (1-2), 303-311.

    Fontana, R., Pistone, G., Rogantin, M.-P., 1997. Algebraic analysis and generation of two-levels designs. Statistica Applicata 9 (1), 15-29.

    Fontana, R., Pistone, G., Rogantin, M. P., 2000. Classification of two-level factorial fractions. J. Statist. Plann. Inference 87 (1), 149-172.

    Holliday, T., Pistone, G., Riccomagno, E., Wynn, H. P., 1999. The application of computational algebraic geometry to the analysis of designed experiments: a case study. Comput. Statist. 14 (2), 213-231.

    Kreuzer, M., Robbiano, L., 2000. Computational Commutative Algebra 1. Springer, Berlin-Heidelberg.

    Kreuzer, M., Robbiano, L., 2005. Computational Commutative Algebra 2. Springer, Berlin-Heidelberg.

    Maruri-Aguilar, H., Notari, R., Riccomagno, E., 2007. On the description and identifiability analysis of mixture designs. Statistica Sinica (accepted for publication).

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