Inference in normal models with commutative orthogonal block structure
Keywords:linear mixed models, commutative Jordan algebra, hypothesis test, variance components, commutative orthogonal block structure
Linear mixed normal models are studied in this paper. Using commutative Jordan algebras, the algebraic properties of these models are studied, as well as optimal estimators, hypothesis tests and confidence regions for fixed and random effects. Model crossing and
nesting is then presented and analyzed.