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

Vera M. Jesus; Paulo Canas Rodrigues; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2007)

- Volume: 27, Issue: 1-2, page 15-25
- ISSN: 1509-9423

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topVera M. Jesus, Paulo Canas Rodrigues, and João Tiago Mexia. "Inference for random effects in prime basis factorials using commutative Jordan algebras." Discussiones Mathematicae Probability and Statistics 27.1-2 (2007): 15-25. <http://eudml.org/doc/277024>.

@article{VeraM2007,

abstract = {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.},

author = {Vera M. Jesus, Paulo Canas Rodrigues, João Tiago Mexia},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {prime basis factorial; commutative Jordan algebras; complete sufficient statistics; UMVUE; confidence regions; orthogonal models; binary operations; factorial models},

language = {eng},

number = {1-2},

pages = {15-25},

title = {Inference for random effects in prime basis factorials using commutative Jordan algebras},

url = {http://eudml.org/doc/277024},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Vera M. Jesus

AU - Paulo Canas Rodrigues

AU - João Tiago Mexia

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

JO - Discussiones Mathematicae Probability and Statistics

PY - 2007

VL - 27

IS - 1-2

SP - 15

EP - 25

AB - 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.

LA - eng

KW - prime basis factorial; commutative Jordan algebras; complete sufficient statistics; UMVUE; confidence regions; orthogonal models; binary operations; factorial models

UR - http://eudml.org/doc/277024

ER -

## References

top- [1] A. Day and R. Mukerjee, Fractional Factorial Plans, Wiley Series in Probability and Statistics (1999). Zbl0930.62081
- [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. Zbl1113.62004
- [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).
- [4] J.T. Mexia, Introdução à Inferência Estatística Linear, Edições Universitárias Lusófonas (1995).
- [5] J.R. Schoot, Matrix Analysis for Statistics, Wiley Interscience (1997).
- [6] J. Seely, Quadratic subspaces and completeness Ann. Math. Stat. (1971), 701-721. Zbl0249.62067