Abstract
The use of a linear model with complex parameters to study factorial designs, has been proposed and detailed by Bailey (1982, 1990) and Kobilinsky (1985, 1990). The complex parameterisation arises quite naturally from the representation theory of abelian groups, which had been used earlier by Foata (1961) and Chakravarti (1976) in the context of factorial designs. This approach has been shown to lead to much simplified calculations to study the efficiency and optimality properties of factorial designs (Collombier, 1989; Kobilinsky and Monod, 1991).
Despite these advantages, the complex linear model is not yet well known in the statistical community. The aim of this paper is to illustrate its usefulness. After a short presentation, we do this by concentrating on a specific problem: the search for an optimal half-fraction of a 2×2×2×p×q factorial design of resolution V.
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© 1994 Springer Science+Business Media Dordrecht
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Monod, H., Kobilinsky, A. (1994). Using the Complex Linear Model to Search for an Optimal Juxtaposition of Regular Fractions. In: Caliński, T., Kala, R. (eds) Proceedings of the International Conference on Linear Statistical Inference LINSTAT ’93. Mathematics and Its Applications, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1004-4_25
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DOI: https://doi.org/10.1007/978-94-011-1004-4_25
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