¹University of Beira Interior, Faculty of Sciences, Department of Mathematics and Center of Mathematics, Covilhã, Portugal. Professor. Email: sandraf@ubi.pt
²University of Beira Interior, Faculty of Sciences, Department of Mathematics and Center of Mathematics, Covilhã, Portugal. Professor. Email: dario@ubi.pt
³University of Beira Interior, Faculty of Sciences, Department of Mathematics and Center of Mathematics, Covilhã, Portugal. Professor. Email: celian@ubi.pt
⁴New University of Lisbon, Faculty of Science and Technology, Department of Mathematics and Center of Mathematics and Its Applications, Covilhã, Portugal. Professor. Email: jtm@fct.unl.pt

Segregation and matching are techniques to estimate variance components in mixed models. A question arising is whether segregation can be applied in situations where matching does not apply. Our motivation for this research relies on the fact that we want an answer to that question and to explore this important class of models that can contribute to the development of mixed models. That is possible using the algebraic structure of mixed models. We present two examples showing that segregation can be applied in situations where matching does not apply.

Key words: Commutative Jordan algebra, Mixed model, Variance components.

La segregación y el emparejamiento son técnicas para estimar las componentes de varianza en modelos mixtos. Una pregunta que ha surgido es si la segregación puede ser aplicada en situaciones en las que el emparejamiento no es aplicable. Nuestra motivación para esta investigación se basa en el hecho de que se quiere una respuesta a esta pregunta y se quiere explorar esta importante clase de modelos con el fin de contribuir al desarrollo de los modelos mixtos. Esto es posible utilizando la estructura algebraica de los modelos mixtos con estructura de bloques ortogonal conmutativa. Se presentan dos ejemplos que muestran que la segregación puede ser aplicada en situaciones donde el emparejamiento no es aplicable.

Palabras clave: álgebra conmutativa Jordan, componentes de varianza, modelo mixto.

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