DOI QR코드

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On the Existence of Maximal Fan Design

Kim, Hyoungsoon;Park, Dongkwon;Kim, KyungHee

  • 발행 : 2002.08.01

초록

An n-point design is maximal fan if all the models with n-terms satisfying the divisibility condition are estimable. Such designs tend to be space filling and look very similar to the ″Latin-hypercube″ designs used in computer experiments. Caboara, Pistone, Riccomago and Wynn (1997) conjectured that a maximal fan design on an integer grid exists for any n and m, where m is the number of factors. In this paper we examine the relationship between maximal fan design and latin-hypercube to give a partial solution for the conjecture.

키워드

Algebraic geometry;Grobner bases;Ideal;Leaf;Maximal fan design

참고문헌

  1. Biometrika v.83 pp.653-666 Generalised confounding with Grobner bases Pistone, G.;Wynn, H.P. https://doi.org/10.1093/biomet/83.3.653
  2. Unpublished Manuscript The fan of an experimental design Caboara, M;Pistone, G.;Riccomagno, E.;H.P. Wynn
  3. Ideal, Varieties, and algorithms Cox, D.;Little, J.;O'Shea, D.
  4. The Theory of Partitions Andrews, G.E.
  5. Technometrics v.3 pp.311-351;449-458 The $2^{k-p}$ fractional factorial designs Box, G.E.P.;Hunter, J.S. https://doi.org/10.2307/1266725
  6. Technometrics v.26 pp.225-232 Minimum aberration $2^{k-p}$designs Fries, A.;Hunter, W.G.