We will discuss orthogonal models and error orthogonal models and their algebraic structure, using as background, commutative Jordan algebras. The role of perfect families of symmetric matrices will be emphasized, since they will play an important part in the construction of the estimators for the relevant parameters. Perfect families of symmetric matrices form a basis for the commutative Jordan algebra they generate. When normality is assumed, these perfect families of symmetric matrices will ensure that the models have complete and sufficient statistics. This will lead to uniformly minimum variance unbiased estimators for the relevant parameters.
@article{bwmeta1.element.doi-10_1515_math-2015-0009,
author = {An\'\i bal Areia and Francisco Carvalho and Jo\~ao T. Mexia},
title = {Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {1307.62139},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0009}
}
Aníbal Areia; Francisco Carvalho; João T. Mexia. Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0009/
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