Geodesic
Inference for random effects in prime basis factorials using commutative Jordan algebras
Discussiones Mathematicae. Probability and Statistics, Tome 27 (2007) no. 1-2, pp. 15-25
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Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.
Keywords: prime basis factorial, commutative Jordan algebras, complete sufficient statistics, UMVUE, confidence regions 
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Jesus, Vera; Rodrigues, Paulo; Mexia, João. Inference for random effects in prime basis factorials using commutative Jordan algebras. Discussiones Mathematicae. Probability and Statistics, Tome 27 (2007) no. 1-2, pp. 15-25. http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a1/

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