Inverting covariance matrices

Czesław Stępniak

Discussiones Mathematicae Probability and Statistics (2006)

  • Volume: 26, Issue: 2, page 163-177
  • ISSN: 1509-9423

Abstract

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Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.

How to cite

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Czesław Stępniak. "Inverting covariance matrices." Discussiones Mathematicae Probability and Statistics 26.2 (2006): 163-177. <http://eudml.org/doc/277048>.

@article{CzesławStępniak2006,
abstract = {Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.},
author = {Czesław Stępniak},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {multi-way classification; cross; hierarchical; balanced; unbalanced; covariance matrix; inverting; linear experiments; Sherman-Morrison-Woodbury formula},
language = {eng},
number = {2},
pages = {163-177},
title = {Inverting covariance matrices},
url = {http://eudml.org/doc/277048},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Czesław Stępniak
TI - Inverting covariance matrices
JO - Discussiones Mathematicae Probability and Statistics
PY - 2006
VL - 26
IS - 2
SP - 163
EP - 177
AB - Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.
LA - eng
KW - multi-way classification; cross; hierarchical; balanced; unbalanced; covariance matrix; inverting; linear experiments; Sherman-Morrison-Woodbury formula
UR - http://eudml.org/doc/277048
ER -

References

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  10. [10] C. Stępniak, A note on estimation of parameters in linear models, Bull. Acad. Polon. Sc. Math., Astr. et Phys. 22 (1974), 1151-1154. Zbl0298.62019
  11. [11] C. Stępniak, Optimal allocation of units in experimental designs with hierarchical and cross classification, Ann. Inst. Statist. Math. A 35 (1983), 461-473. Zbl0553.62065
  12. [12] C. Stępniak, Inversion of covariance matrices: explicit formulae, SIAM J. Matrix Anal. Appl. 12 (1991), 577-580. Zbl0734.15006
  13. [13] C. Stępniak and M. Niezgoda, Inverting covariance matrices in unbalanced hierarchical models, J. Statist. Comput. Simul. 51 (1995), 215-221. Zbl0842.62050
  14. [14] D.M. VanLeeuwen, D.S. Birkes and J.F. Seely, Balance and orthogonality in designs for mixed classification models, Ann. Statist. 2 (1999), 1927-1947. Zbl0963.62059
  15. [15] R. Zmyślony and H. Drygas, Jordan algebras and Bayesian quadratic estimation of variance components, Linear Algebra Appl. 168 (1992), 259-275. Zbl0760.62068

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