Estimators and tests for variance components in cross nested orthogonal designs

Miguel Fonseca; João Tiago Mexia; Roman Zmyślony

Discussiones Mathematicae Probability and Statistics (2003)

  • Volume: 23, Issue: 2, page 175-201
  • ISSN: 1509-9423

Abstract

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Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.

How to cite

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Miguel Fonseca, João Tiago Mexia, and Roman Zmyślony. "Estimators and tests for variance components in cross nested orthogonal designs." Discussiones Mathematicae Probability and Statistics 23.2 (2003): 175-201. <http://eudml.org/doc/287757>.

@article{MiguelFonseca2003,
abstract = {Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.},
author = {Miguel Fonseca, João Tiago Mexia, Roman Zmyślony},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {hypothesis testing; generalized F distribution; adaptative test; nested orthogonal designs; generalized distribution; adaptive test; Jordan algebras},
language = {eng},
number = {2},
pages = {175-201},
title = {Estimators and tests for variance components in cross nested orthogonal designs},
url = {http://eudml.org/doc/287757},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Miguel Fonseca
AU - João Tiago Mexia
AU - Roman Zmyślony
TI - Estimators and tests for variance components in cross nested orthogonal designs
JO - Discussiones Mathematicae Probability and Statistics
PY - 2003
VL - 23
IS - 2
SP - 175
EP - 201
AB - Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.
LA - eng
KW - hypothesis testing; generalized F distribution; adaptative test; nested orthogonal designs; generalized distribution; adaptive test; Jordan algebras
UR - http://eudml.org/doc/287757
ER -

References

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  2. [2] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discuss. Math.-Probability and Satatistics 1,2 (2002), 37-51. Zbl1037.62004
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  9. [9] T.A. Severini, Likelihood Methods in Statistics, Oxford University Press 2000. 
  10. [10] W.H. Steeb, Kronecker Product and Applications, Manheim 1991. 
  11. [11] R. Zmyślony, Completeness for a family of normal distributions, Mathematical Statistics, Banach Cent. Publ. 6 (1980), 355-357. Zbl0464.62003
  12. [12] A. Michalski and R. Zmyślony, Testing hypotheses for variance components in mixed linear models, Statistics (3-4) 27 (1996), 297-310. Zbl0842.62059
  13. [13] R. Zmyślony and S. Zontek, On robust estimation of variance components via von Mises functionals, Discuss. Math.-Algebra and Stoch. Methods, 15 (2) (1995), 349-362. Zbl0842.62021
  14. [14] A. Michalski and R. Zmyślony, Testing hypotheses for linear functions of parameters in mixed linear models, Tatra Mt. Math. Publ. 17 (1999), 103-110. Zbl0987.62012
  15. [15] S. Zontek, Robust estimation in linear models to spatially located sensors and random input, Tatra Mountain Publications 17 (1999), 301-310. Zbl1067.62527

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