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Plans sphériques de force t et applications en statistique

Abstract : This work is made of two parts, a theorical one and an applied one, and is about the combined use of combinatoric and algebraic tools to design and analyze experiments. We lay the stress on polynomial characterizations of weakly invariant designs and set a framework to solve these systems of polynomial equations using real algebraic geometry and the link between the realstellensatz and semi definite programming tools. We focus too on the methodology of response surfaces and more especially on rotatable ones, which leads us to study intensively the designs whose support points lie on a sphere. The main advantages of this approach are its various potential applications, its automatic use and the computation of the exact coordinates of the support points of the designs as well as the complete computation of the aliasings. On the contrary, a numeric way of designing weakly invariant designs would miss our point since we would be unable to classify the designs up to an orthogonal isometry and to spotlight all the aliasings that will appear with Euclidean designs of small sizes. Yet, a minute and accurate knowledge of the aliasings is a major help for the practitioners since they will no longer be limited to use low degree polynomial models to analyze their datasets. Many rotatable designs are produced using this methodology. Their properties and the programs that were used to find them are also depicted.
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https://tel.archives-ouvertes.fr/tel-00188330
Contributor : Frédéric Bertrand <>
Submitted on : Wednesday, June 11, 2008 - 12:52:32 PM
Last modification on : Friday, June 19, 2020 - 9:10:04 AM
Long-term archiving on: : Thursday, September 23, 2010 - 5:14:50 PM

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  • HAL Id : tel-00188330, version 3

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Frédéric Bertrand. Plans sphériques de force t et applications en statistique. Mathématiques [math]. Université Louis Pasteur - Strasbourg I, 2007. Français. ⟨NNT : 2007STR13123⟩. ⟨tel-00188330v3⟩

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