Weakly Invariant Designs, Rotatable Designs and Polynomial Designs

Frédéric Bertrand (1)

1 IRMA - Institut de Recherche Mathématique Avancée

In this article, we state a polynomial characterization of weakly invariant designs and show how to derive the construction of weakly invariant designs from the construction of rotatable designs using a new moment generating function introduced to that purpose. We apply the methods of computational commutative algebra to provide existence results for spherical rotatable polynomial designs in R3. These designs can be of use in various settings such as response surface methodology or three-dimensional shape analysis.

Mots clés: Design of experiments; response surface designs; optimal designs; polynomial designs; weak invariance; rotatability; moment generating function; algebraic statistics; Groebner bases; computational commutative algebra; real algebraic sets; semidefinite programming

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Frédéric Bertrand. Weakly Invariant Designs, Rotatable Designs and Polynomial Designs. Contemporary mathematics, 2010, 516, pp.49-60. ⟨10.1090/conm/516⟩. ⟨hal-00493572⟩