Error orthogonal models: Structure, Operations and Inference
Carla Santos · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2012
In this thesis, we develop the theory of Error-Orthogonal Models availing ourselves of the identity of these models and those with Commutative Orthogonal Block Structure. Thus our treatment will rest on the algebraic structure of the models. In our development we consider: the estimation of variance components; crossing and nesting of models; model joining, in which observations vectors obtained separately are jointly analyzed; step nesting which require much less observations than the corresponding usual models. To broaden our treatment we also consider L Extensions of Error-Orthogonal models. In this way, we may consider interesting cases such as models otherwise balanced with different numbers of replicates for the treatments. Last we include normality. We will be interested in obtaining sufficient statistics as well as conditions for them to be complete. We will carry out inference and consider orthogonal L extensions.