Weakly invariant designs and polynomial designs

Frédéric Bertrand (1)

1 IRMA - Institut de Recherche Mathématique Avancée

A design is said to be a polynomial design if the coordinates of the points supporting the design are the solutions of a system of polynomial equalities or inequalities ; such a system can always be solved using semidefinite programming or Gröbner bases. Many praised properties of designs, such as alphabetic optimality and orthogonal blocking, can be easily stated in the framework of polynomial designs. The same holds for G−weakly invariant designs, G being any compact group of matrices, since we show G−weak invariance boils to H-weak invariance, with H a subgroup of the orthogonal group Ov of Rv.

Mots clés: Semidefinite prgramming; Design of experiments; Algebraic statistics; Weakly invariant designs; Rotatable designs; Polynomial designs; Gröbner bases; Semidefinite prgramming.

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

Frédéric Bertrand. Weakly invariant designs and polynomial designs. Joint Meeting of the Statistical Society of Canada and the Société Française de Statistique, May 2008, Ottawa, Canada. ⟨hal-00287609⟩