# Variance components estimation in generalized orthogonal models

Célia Fernandes; Paulo Ramos; Sandra Saraiva Ferreira; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2007)

- Volume: 27, Issue: 1-2, page 99-115
- ISSN: 1509-9423

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topCélia Fernandes, et al. "Variance components estimation in generalized orthogonal models." Discussiones Mathematicae Probability and Statistics 27.1-2 (2007): 99-115. <http://eudml.org/doc/277043>.

@article{CéliaFernandes2007,

abstract = {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.},

author = {Célia Fernandes, Paulo Ramos, Sandra Saraiva Ferreira, João Tiago Mexia},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {generalized orthogonal models; variance components; generalized cross nesting designs},

language = {eng},

number = {1-2},

pages = {99-115},

title = {Variance components estimation in generalized orthogonal models},

url = {http://eudml.org/doc/277043},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Célia Fernandes

AU - Paulo Ramos

AU - Sandra Saraiva Ferreira

AU - João Tiago Mexia

TI - Variance components estimation in generalized orthogonal models

JO - Discussiones Mathematicae Probability and Statistics

PY - 2007

VL - 27

IS - 1-2

SP - 99

EP - 115

AB - 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.

LA - eng

KW - generalized orthogonal models; variance components; generalized cross nesting designs

UR - http://eudml.org/doc/277043

ER -

## References

top- [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. Zbl1037.62004
- [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. Zbl0804.62001
- [7] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310. Zbl0842.62059
- [8] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 1999. Zbl0987.62012
- [9] J. Nelder, The interpretation of negative components of variance, Biometrika 41 (1954), 544-548. Zbl0056.12703

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