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

Abstract

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The model y = ∑ j = 1 w X j β ̲ j + e ̲ 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.

How to cite

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Célia 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

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  1. [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. [2] C. Fernandes, P. Ramos and J.T. Mexia, Optimization of Nested Step Designs, Biometrical Letters 42-2 (2005), 143-151. 
  3. [3] C. Fernandes, P. Ramos and J.T. Mexia, Evenness conditions for four cross nested models, Biometrical Letters 43-2 (2006), 109-130. 
  4. [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. [5] E.L. Lehmann, Testing Statistical Hypotesis, Jonh Willey and Sons, New York 1952. 
  6. [6] J. Malley, Statistical Applications of Jordan Algebras, Springer-Verlag 1994. Zbl0804.62001
  7. [7] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310. Zbl0842.62059
  8. [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. [9] J. Nelder, The interpretation of negative components of variance, Biometrika 41 (1954), 544-548. Zbl0056.12703

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