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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Canonic inference and commutative orthogonal block structure

100%
Carvalho F., Mexia J., Oliveira M.
Discussiones Mathematicae Probability and Statistics
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2008
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tom 28
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nr 2
171-181
EN
It is shown how to define the canonic formulation for orthogonal models associated to commutative Jordan algebras. This canonic formulation is then used to carry out inference. The case of models with commutative orthogonal block structures is stressed out.
2
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ANOVA using commutative Jordan algebras, an application

100%
Rodrigues P., Mexia J.
Discussiones Mathematicae Probability and Statistics
|
2006
|
tom 26
|
nr 2
179-191
EN
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.
3
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Joint estimation for normal orthogonal mixed models

100%
de Jesus V., Ferreira S., Mexia J.
Discussiones Mathematicae Probability and Statistics
|
2007
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tom 27
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nr 1-2
5-13
EN
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.
4
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Inference for random effects in prime basis factorials using commutative Jordan algebras

88%
Jesus V., Rodrigues P., Mexia J.
Discussiones Mathematicae Probability and Statistics
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2007
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tom 27
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nr 1-2
15-25
EN
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.
5
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Algebraic structureof step nesting designs

88%
Fernandes C., Ramos P., Mexia J.
Discussiones Mathematicae Probability and Statistics
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2010
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tom 30
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nr 2
221-235
EN
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 we introduce the cartesian product of commutative Jordan algebras.
6
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Algebraic structure for the crossing of balanced and stair nested designs

75%
Fernandes C., Ramos P., Mexia J.
Discussiones Mathematicae Probability and Statistics
|
2014
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tom 34
|
nr 1-2
71-88
EN
Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.
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