Variance components estimation in generalized orthogonal models
Discussiones Mathematicae. Probability and Statistics, Tome 27 (2007) no. 1-2, pp. 99-115.

Voir la notice de l'article provenant de la source Library of Science

The model y = ∑_j=1^w X_j β̲_j + e̲ is generalized orthogonal if the orthogonal projection matrices on the range spaces of matrices X_j, j = 1, ..., w, commute. Unbiased estimators are obtained for the variance components of such models with cross-nesting.
Keywords: generalized orthogonal models, variance components, generalized cross nesting designs
@article{DMPS_2007_27_1-2_a5,
     author = {Fernandes, C\'elia and Ramos, Paulo and Ferreira, Sandra and Mexia, Jo\~ao},
     title = {Variance components estimation in generalized orthogonal models},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {99--115},
     publisher = {mathdoc},
     volume = {27},
     number = {1-2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a5/}
}
TY  - JOUR
AU  - Fernandes, Célia
AU  - Ramos, Paulo
AU  - Ferreira, Sandra
AU  - Mexia, João
TI  - Variance components estimation in generalized orthogonal models
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2007
SP  - 99
EP  - 115
VL  - 27
IS  - 1-2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a5/
LA  - en
ID  - DMPS_2007_27_1-2_a5
ER  - 
%0 Journal Article
%A Fernandes, Célia
%A Ramos, Paulo
%A Ferreira, Sandra
%A Mexia, João
%T Variance components estimation in generalized orthogonal models
%J Discussiones Mathematicae. Probability and Statistics
%D 2007
%P 99-115
%V 27
%N 1-2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a5/
%G en
%F DMPS_2007_27_1-2_a5
Fernandes, Célia; Ramos, Paulo; Ferreira, Sandra; Mexia, João. Variance components estimation in generalized orthogonal models. Discussiones Mathematicae. Probability and Statistics, Tome 27 (2007) no. 1-2, pp. 99-115. http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a5/

[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.

[2] C. Fernandes, P. Ramos and J.T. Mexia, Optimization of Nested Step Designs, Biometrical Letters 42-2 (2005), 143-151.

[3] C. Fernandes, P. Ramos and J.T. Mexia, Evenness conditions for four cross nested models, Biometrical Letters 43-2 (2006), 109-130.

[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.

[5] E.L. Lehmann, Testing Statistical Hypotesis, Jonh Willey and Sons, New York 1952.

[6] J. Malley, Statistical Applications of Jordan Algebras, Springer-Verlag 1994.

[7] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.

[8] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 1999.

[9] J. Nelder, The interpretation of negative components of variance, Biometrika 41 (1954), 544-548.