On optimal third order rotatable designs

Draper, Norman R.; Heiligers, Berthold; Pukelsheim, Friedrich

doi:10.1007/bf00054798

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1998

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Cited by 5 publications

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“…A similar approach to non-mixture response surface models was used successfully in Draper, Ga ke and Pukelsheim (1991), Draper and Pukelsheim (1994), and Draper, Heiligers and Pukelsheim (1996) see also Chapter 15 in Pukelsheim (1993).…”

Section: Introductionmentioning

confidence: 99%

Mixture models based on homogeneous polynomials

Draper

Pukelsheim

1998

Journal of Statistical Planning and Inference

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Models for mixtures of ingredients are typically tted by S c he e's canonical model forms. An alternative representation is discussed which o ers attractive symmetries, compact notation and homogeneous model functions. It is based on the Kronecker algebra of vectors and matrices, used successfully in previous response surface work. These alternative polynomials are contrasted with those of Sche e, and ideas of synergism and model reduction are connected together in both algebras. Sche e's \special cubic" is shown to be sensible in both algebras. Mathematics Subject Classi cations: 62K15 62J05Keywords: Designs for mixtures First order models Kronecker product Mixture amount models Sche e canonical polynomial Second order models Synergism Third order models.

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Section: Introductionmentioning

confidence: 99%