Binary Operations on Prime Basis Factorials and Their Fractional Replicates
by
Vera Jesus
New University of Lisbon
Coauthors: João Tiago Mexia

Among orthogonal models, the prime basis factorials and their fractional replicates are distinguished for their flexibility. Commutative Jordan algebras were used by Seely (1971), in the study of normal orthogonal models. We are introducing the notion of a model strictly associated to a commutative Jordan algebra which enables us to obtain in a straightforward way uniformly minimum variance unbiased estimators, UMVUE.Binary operations on commutative Jordan algebras are used to define product and nested models as well as to extend the study of crossing and nesting of prime basis factorial to their fractional eplicates, where the factors have arbitrary number of levels.

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Date received: July 22, 2007