Linear model genealogical tree application to an odontology experiment

Ricardo Covas

Discussiones Mathematicae Probability and Statistics (2007)

  • Volume: 27, Issue: 1-2, page 47-77
  • ISSN: 1509-9423

Abstract

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Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras and mixed linear models give to practitioners.

How to cite

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Ricardo Covas. "Linear model genealogical tree application to an odontology experiment." Discussiones Mathematicae Probability and Statistics 27.1-2 (2007): 47-77. <http://eudml.org/doc/277027>.

@article{RicardoCovas2007,
abstract = {Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras and mixed linear models give to practitioners.},
author = {Ricardo Covas},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {commutative Jordan algebra; binary operations; Kronecker matrix product; lattice; projectors},
language = {eng},
number = {1-2},
pages = {47-77},
title = {Linear model genealogical tree application to an odontology experiment},
url = {http://eudml.org/doc/277027},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Ricardo Covas
TI - Linear model genealogical tree application to an odontology experiment
JO - Discussiones Mathematicae Probability and Statistics
PY - 2007
VL - 27
IS - 1-2
SP - 47
EP - 77
AB - Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras and mixed linear models give to practitioners.
LA - eng
KW - commutative Jordan algebra; binary operations; Kronecker matrix product; lattice; projectors
UR - http://eudml.org/doc/277027
ER -

References

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  1. [1] R. Covas, Inferência Semi-Bayesiana e Modelos de Componentes de Variância - Tese de Mestrado, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa (document in Portuguese Language) 2003. 
  2. [2] R. Covas, Orthogonal Mixed Models and Commutative Jordan Algebras - PhD Thesis, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa 2007. 
  3. [3] R. Covas, J.T. Mexia and R. Zmyślony, Lattices of Jordan algebras, To be published in Linear Algebra and Aplications 2007. 
  4. [4] S. Ferreira, Inferência para Modelos Ortogonais com Segregação, Tese de Doutoramento - Universidade da Beira Interior (document in Portuguese Language) 2006. 
  5. [5] M. Fonseca, J.T. Mexia and R. Zmyślony, Binary Operations on Jordan Algebras and Orthogonal Normal Models, Linear Algebra and it's Applications 417 (1) (2006), 75-86. Zbl1113.62004
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  7. [7] P. Jordan, J. von Neumann and E. Wigner, On an Algebraic Generalization of the Quantum Mechanical Formulation, Ann. Math. 36 (1934), 26-64. Zbl60.0902.02
  8. [8] J.D. Malley, Optimal Unbiased Estimation of Variance Components, Lecture Notes in Statist. 39, Springer-Verlag, Berlin 1986. Zbl0604.62064
  9. [9] A. Michalski and R. Zmyślony, Testing Hypothesis for Variance components in Mixed Linear Models Statistics 27 (3-4) (1996), 297-310. Zbl0842.62059
  10. [10] A. Michalski and R. Zmyślony, Testing Hypothesis for Linear Fuctions of Parameters in Mixed Linear Models, Tatra Mt. Math. Publ. 17 (1999), 103-110. Zbl0987.62012
  11. [11] D.C. Montgomery, Design and Analysis of Experiments - 6th Edition, Wiley 2004. 
  12. [12] C.R. Rao and J. Kleffe, Estimation of Variance Components and Applications, North-Holland, Elsevier - Amsterdam 1988. Zbl0645.62073
  13. [13] J. Seely, Quadratic Subspaces and Completeness, Ann. Math. Stat. 42 N2 (1971), 710-721. Zbl0249.62067
  14. [14] J. Seely, Completeness for a family of multivariate normal distribution, Ann. Math. Stat. 43 (1972), 1644-1647. Zbl0257.62018
  15. [15] J. Seely, Minimal sufficient statistics and completeness for multivariate normal families, Sankhyã 39 (1977), 170-185. Zbl0409.62004
  16. [16] R. Zmyślony, On estimation of parameters in linear models, Applicationes Mathematicae XV 3 (1976), 271-276. Zbl0401.62049

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