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Advisor(s)
Abstract(s)
Models with commutative orthogonal block structure, COBS, have orthogonal
block structure, OBS, and their least square estimators for estimable vectors are,
as it will be shown, best linear unbiased estimator, BLUE. Commutative Jordan algebras
will be used to study the algebraic structure of the models and to define special
types of models for which explicit expressions for the estimation of variance components
are obtained. Once normality is assumed, inference using pivot variables is quite
straightforward. To illustrate this class of models we will present unbalanced examples
before considering families of models. When the models in a family correspond to the treatments of a base design, the family is structured. It will be shown how, under quite
general conditions, the action of the factors in the base design on estimable vectors,
can be studied.
Description
Keywords
Commutative orthogonal block structure Commutative Jordan algebras Estimation Mixed linear models