Binary operations on Jordan algebras and orthogonal normal models

Jordan algebras are used to present normal orthogonal models in a canonical form. Binary operations are defined on these algebras, which enable us to build complex models based on simpler ones. Properties of these operations and their relation with balanced models are studied. The canonical model formulation is interesting because it leads to complete sufficient statistics. These statistics are then used to obtain estimators in order to test hypothesis on the model parameters.