Binary operations on orthogonal models, application to prime basis factorials and fractional replicates

Commutative Jordan algebras (CJA) are used in the study of orthogonal models either simple or de20 rived through model crossing and model nesting. Once normality is assumed, UMVUE are obtained for relevant parameters. The general treatment is then applied to models obtained from prime basis factorials or their fractional replicates. Besides model crossing and nesting, factor merging is considered. In this way we may extend our results to factors with whatever number of levels instead of factors whose numbers of levels are powers of the same prime. AMS Subject Classification: 62J12; 62K15; 17C50.