Strictly associated models, prime basis factorials: an application

Francisco Carvalho

Discussiones Mathematicae Probability and Statistics (2011)

  • Volume: 31, Issue: 1-2, page 77-86
  • ISSN: 1509-9423

Abstract

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Mixed models will be considered using the Commutative Jordan Algebra of Symmetric matrices approach. Prime basis factorial models will now be considered in the framework provided by Commutative Jordan Algebra of Symmetric matrices. This will enable to obtain fractional replicates when the number of levels is neither a prime or a power of a prime. We present an application to the effect of lidocaine, at an enzymatic level, on the heart muscle of beagle dogs

How to cite

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Francisco Carvalho. "Strictly associated models, prime basis factorials: an application." Discussiones Mathematicae Probability and Statistics 31.1-2 (2011): 77-86. <http://eudml.org/doc/277062>.

@article{FranciscoCarvalho2011,
abstract = {Mixed models will be considered using the Commutative Jordan Algebra of Symmetric matrices approach. Prime basis factorial models will now be considered in the framework provided by Commutative Jordan Algebra of Symmetric matrices. This will enable to obtain fractional replicates when the number of levels is neither a prime or a power of a prime. We present an application to the effect of lidocaine, at an enzymatic level, on the heart muscle of beagle dogs},
author = {Francisco Carvalho},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {COBS; strictly associated models; prime basis factorials; inference},
language = {eng},
number = {1-2},
pages = {77-86},
title = {Strictly associated models, prime basis factorials: an application},
url = {http://eudml.org/doc/277062},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Francisco Carvalho
TI - Strictly associated models, prime basis factorials: an application
JO - Discussiones Mathematicae Probability and Statistics
PY - 2011
VL - 31
IS - 1-2
SP - 77
EP - 86
AB - Mixed models will be considered using the Commutative Jordan Algebra of Symmetric matrices approach. Prime basis factorial models will now be considered in the framework provided by Commutative Jordan Algebra of Symmetric matrices. This will enable to obtain fractional replicates when the number of levels is neither a prime or a power of a prime. We present an application to the effect of lidocaine, at an enzymatic level, on the heart muscle of beagle dogs
LA - eng
KW - COBS; strictly associated models; prime basis factorials; inference
UR - http://eudml.org/doc/277062
ER -

References

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  1. [1] M. Fonseca, J.T. Mexia and R. Zmyślony, Binary Operation on Jordan algebras and orthogonal normal models, Linear Algebra and its Applications 417 (2006) 75-86. Zbl1113.62004
  2. [2] V.M. Jesus, J.T. Mexia and M.M. Oliveira, Binary Operations on Prime Basis Factorials, Biometric Letters 46 (1) (2009) 1-14. 
  3. [3] V.M. Jesus, J.T. Mexia, M. Fonseca and R. Zmyślony, Binary Operations and Canonical Forms for Factorial and Related Models, Linear Algebra and its Applications 430 (2009) 2781-2797. Zbl1160.62072
  4. [4] P. Jordan, J. von Neumann and E. Wigner, On the algebraic generalization of the quantum mechanical formalism, Ann. of Math. 36 (1934) 26-64. Zbl60.0902.02
  5. [5] E.L. Lehman, Testing Statistical Hypothesis (John Wiley & Son, 2nd ed., 1986). 
  6. [6] D.C. Montegomery, Design and Analysis of Experiments (John Wiley & Sons, 2005). 
  7. [7] J. Seely, Linear spaces and unbiased estimators, The Annals of Mathematical Statistics 41 (1970a) 1735-1745. Zbl0263.62041
  8. [8] J. Seely, Linear spaces and unbiased estimators. Application to a mixed linear model, The Annals of Mathematical Statistics 41 (1970b) 1735-1745. Zbl0263.62041
  9. [9] J. Seely, Quadratic subspaces and completeness, The Annals of Mathematical Statistics 42 (1971) 710-721. Zbl0249.62067
  10. [10] J. Seely and G. Zyskind, Linear spaces and minimum variance estimators, The Annals of Mathematical Statistics 42 (1971) 691-703. Zbl0217.51602

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