Geodesic
Algebraic structureof step nesting designs
Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 221-235

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Step nesting designs may be very useful since they require fewer observations than the usual balanced nesting models. The number of treatments in balanced nesting design is the product of the number of levels in each factor. This number may be too large. As an alternative, in step nesting designs the number of treatments is the sum of the factor levels. Thus these models lead to a great economy and it is easy to carry out inference. To study the algebraic structure of step nesting designs we introduce the cartesian product of commutative Jordan algebras.
Keywords: commutative Jordan algebras, cartesian product of commutative Jordan algebras, step nesting, variance components, UMVUE 
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Fernandes, Célia; Ramos, Paulo; Mexia, João. Algebraic structureof step nesting designs. Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 221-235. http://geodesic.mathdoc.fr/item/DMPS_2010_30_2_a3/