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.
@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/
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