The model is generalized orthogonal if the orthogonal projection matrices on the range spaces of matrices , j = 1, ..., w, commute. Unbiased estimators are obtained for the variance components of such models with cross-nesting.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1090, author = {C\'elia Fernandes and Paulo Ramos and Sandra Saraiva Ferreira and Jo\~ao Tiago Mexia}, title = {Variance components estimation in generalized orthogonal models}, journal = {Discussiones Mathematicae Probability and Statistics}, volume = {27}, year = {2007}, pages = {99-115}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1090} }
Célia Fernandes; Paulo Ramos; Sandra Saraiva Ferreira; João Tiago Mexia. Variance components estimation in generalized orthogonal models. Discussiones Mathematicae Probability and Statistics, Tome 27 (2007) pp. 99-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1090/
[000] [1] C. Fernandes, P. Ramos and J.T. Mexia, Optimização de Delineamentos em Escada Simples, Actas do XII Congresso Anual da SPE (2005), 247-253.
[001] [2] C. Fernandes, P. Ramos and J.T. Mexia, Optimization of Nested Step Designs, Biometrical Letters 42-2 (2005), 143-151.
[002] [3] C. Fernandes, P. Ramos and J.T. Mexia, Evenness conditions for four cross nested models, Biometrical Letters 43-2 (2006), 109-130.
[003] [4] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distributions for the generalized F tests, Discussiones Mathematicae - Probability and Statistics 22 (2002), 37-51. | Zbl 1037.62004
[004] [5] E.L. Lehmann, Testing Statistical Hypotesis, Jonh Willey and Sons, New York 1952.
[005] [6] J. Malley, Statistical Applications of Jordan Algebras, Springer-Verlag 1994. | Zbl 0804.62001
[006] [7] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310. | Zbl 0842.62059
[007] [8] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 1999. | Zbl 0987.62012
[008] [9] J. Nelder, The interpretation of negative components of variance, Biometrika 41 (1954), 544-548. | Zbl 0056.12703