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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1086,
author = {Vera M. Jesus and Paulo Canas Rodrigues and Jo\~ao Tiago Mexia},
title = {Inference for random effects in prime basis factorials using commutative Jordan algebras},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {27},
year = {2007},
pages = {15-25},
zbl = {1211.62139},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1086}
}
Vera M. Jesus; Paulo Canas Rodrigues; João Tiago Mexia. Inference for random effects in prime basis factorials using commutative Jordan algebras. Discussiones Mathematicae Probability and Statistics, Tome 27 (2007) pp. 15-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1086/
[000] [1] A. Day and R. Mukerjee, Fractional Factorial Plans, Wiley Series in Probability and Statistics (1999). | Zbl 0930.62081
[001] [2] 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. | Zbl 1113.62004
[002] [3] J.T. Mexia, Standardized Orthogonal Matrices and the Decomposition of the sum of Squares for Treatments, Trabalhos de Investigação nº2, Departamento de Matemática, FCT-UNL (1988).
[003] [4] J.T. Mexia, Introdução à Inferência Estatística Linear, Edições Universitárias Lusófonas (1995).
[004] [5] J.R. Schoot, Matrix Analysis for Statistics, Wiley Interscience (1997).
[005] [6] J. Seely, Quadratic subspaces and completeness Ann. Math. Stat. (1971), 701-721. | Zbl 0249.62067