Displaying similar documents to “Canonic inference and commutative orthogonal block structure”

ANOVA using commutative Jordan algebras, an application

Paulo Canas Rodrigues, João Tiago Mexia (2006)

Discussiones Mathematicae Probability and Statistics

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Binary operations on commutative Jordan algebras are used to carry out the ANOVA of a two layer model. The treatments in the first layer nests those in the second layer, that being a sub-model for each treatment in the first layer. We present an application with data retried from agricultural experiments.

Inference for random effects in prime basis factorials using commutative Jordan algebras

Vera M. Jesus, Paulo Canas Rodrigues, João Tiago Mexia (2007)

Discussiones Mathematicae Probability and Statistics

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Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.

Algebraic structureof step nesting designs

Célia Fernandes, Paulo Ramos, João Tiago Mexia (2010)

Discussiones Mathematicae Probability and Statistics

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Step nesting designs may be very useful since they require fewer observations than the usual balanced nesting models. The number of treatments in balanced nesting design is the product of the number of levels in each factor. This number may be too large. As an alternative, in step nesting designs the number of treatments is the sum of the factor levels. Thus these models lead to a great economy and it is easy to carry out inference. To study the algebraic structure of step nesting designs...

Linear model genealogical tree application to an odontology experiment

Ricardo Covas (2007)

Discussiones Mathematicae Probability and Statistics

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Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras and mixed linear models give to practitioners.

Joint estimation for normal orthogonal mixed models

Vera de Jesus, Sandra Saraiva Ferreira, João Tiago Mexia (2007)

Discussiones Mathematicae Probability and Statistics

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Commutative Jordan algebras are used to express the structure of mixed orthogonal models and to derive complete sufficient statistics. From these statistics, UMVUE, (Uniformly Minimum Variance Unbiased Estimators), are derived for the relevant parameters, first of single models then of several such models. These models may correspond to experiments designed separately so our results may be seen as a contribution to this meta-analysis.

Commutative directoids with sectional involutions

Ivan Chajda (2007)

Discussiones Mathematicae - General Algebra and Applications

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The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.

The Jordan structure of CSL algebras

Fangyan Lu (2009)

Studia Mathematica

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We show that every Jordan isomorphism between CSL algebras is the sum of an isomorphism and an anti-isomorphism. Also we show that each Jordan derivation of a CSL algebra is a derivation.