Inverting covariance matrices
Czesław Stępniak
Discussiones Mathematicae Probability and Statistics, Tome 26 (2006), p. 163-177 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:277048
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1080,
     author = {Czes\l aw St\k epniak},
     title = {Inverting covariance matrices},
     journal = {Discussiones Mathematicae Probability and Statistics},
     volume = {26},
     year = {2006},
     pages = {163-177},
     zbl = {1132.15006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1080}
}
Czesław Stępniak. Inverting covariance matrices. Discussiones Mathematicae Probability and Statistics, Tome 26 (2006) pp. 163-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1080/

[000] [1] G.H. Golub and C.F. Van Loan, Matrix Computation, Sec. Edition, J. Hopkins Univ. Press, Baltimore 1989.

[001] [2] F.A. Graybill, Matrices with Application in Statistics, Sec. Edition, Wadsworth, Belmont, CA 1983. | Zbl 0496.15002

[002] [3] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge Univ. Press, Cambridge 1985. | Zbl 0576.15001

[003] [4] J. Jiang, Dispersion matrix in balanced mixed ANOVA models, Linear Algebra Appl. 382 (2004), 211-219. | Zbl 1041.62057

[004] [5] J. Kleffe and B. Seifert, Computation of variance components by MINQUE method, J. Multivariate Anal. 18 (1986), 107-116. | Zbl 0583.62068

[005] [6] L.R. LaMotte, Notes on the covariance matrix of a random nested ANOVA model, Ann. Math. Statist. 43 (1972), 659-662. | Zbl 0261.62053

[006] [7] C.R. Rao, Linear Statistical Inference and Its Applications, Sec. Edition, J. Wiley, New York 1973. | Zbl 0256.62002

[007] [8] S.R. Searle, G. Casella and C. McCulloch, Variance Components, J. Wiley, New York 1992.

[008] [9] J. Seely, Quadratic subspaces and completeness, Ann. Math. Statist. 42 (1971), 710-721. | Zbl 0249.62067

[009] [10] C. Stępniak, A note on estimation of parameters in linear models, Bull. Acad. Polon. Sc. Math., Astr. et Phys. 22 (1974), 1151-1154. | Zbl 0298.62019

[010] [11] C. Stępniak, Optimal allocation of units in experimental designs with hierarchical and cross classification, Ann. Inst. Statist. Math. A 35 (1983), 461-473. | Zbl 0553.62065

[011] [12] C. Stępniak, Inversion of covariance matrices: explicit formulae, SIAM J. Matrix Anal. Appl. 12 (1991), 577-580. | Zbl 0734.15006

[012] [13] C. Stępniak and M. Niezgoda, Inverting covariance matrices in unbalanced hierarchical models, J. Statist. Comput. Simul. 51 (1995), 215-221. | Zbl 0842.62050

[013] [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. | Zbl 0963.62059

[014] [15] R. Zmyślony and H. Drygas, Jordan algebras and Bayesian quadratic estimation of variance components, Linear Algebra Appl. 168 (1992), 259-275. | Zbl 0760.62068