Geodesic
ANOVA using commutative Jordan algebras, an application
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 179-191.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: commutative Jordan algebras, variance components, orthogonal models, ANOVA 
@article{DMPS_2006_26_2_a4,
     author = {Rodrigues, Paulo and Mexia, Jo\~ao},
     title = {ANOVA using commutative {Jordan} algebras, an application},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {179--191},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2006},
     zbl = {1133.62341},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a4/}
}
TY  - JOUR
AU  - Rodrigues, Paulo
AU  - Mexia, João
TI  - ANOVA using commutative Jordan algebras, an application
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2006
SP  - 179
EP  - 191
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a4/
LA  - en
ID  - DMPS_2006_26_2_a4
ER  - 
%0 Journal Article
%A Rodrigues, Paulo
%A Mexia, João
%T ANOVA using commutative Jordan algebras, an application
%J Discussiones Mathematicae. Probability and Statistics
%D 2006
%P 179-191
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a4/
%G en
%F DMPS_2006_26_2_a4
Rodrigues, Paulo; Mexia, João. ANOVA using commutative Jordan algebras, an application. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 179-191. http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a4/

[1] D.J.C. Ferreira, Variáveis pivot indutoras e componentes de variância em modelos normais ortogonais, PhD thesis - Covilhã 2005.

[2] M. Fonseca, J.T. Mexia and R. Zmyślony, An Application to Grapevines of Estimating and Testing of Variance Components, Biometrical Letters 40 (2002), 1-7.

[3] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimators and Tests for Variance Components in Cross Nested Orthogonal Models, Discussiones Mathematicae - Probability and Statistics 23 (2003), 173-201.

[4] M. Fonseca, J.T. Mexia and R. Zmyślony, Binary Operations on Jordan Algebras and Orthogonal Normal Models, Linear Algebra and Its Applications 417 (2006), 75-86.

[5] A.I. Khuri, T. Mathew and B.K. Sinha, Statistical tests for mixed linear models, John Wiley and Sons, New York 1997.

[6] P.C. Rodrigues and J.T. Mexia, Estimação de Componentes de Variância em Modelos Equilibrados com Cruzamento e Encaixe, in Estatística Jubilar-Actas do XII Congresso Anual da SPE 2005.

[7] J. Seely, Quadratic subspaces and completeness, Ann. Math. Stat. 42 (1971), 710-721.