Generalized F tests in models with random perturbations: the gamma case

Célia Maria Pinto Nunes; Sandra Maria Bargão Saraiva Ferreira; Dário Jorge da Conceição Ferreira

Discussiones Mathematicae Probability and Statistics (2009)

  • Volume: 29, Issue: 2, page 185-197
  • ISSN: 1509-9423

Abstract

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Generalized F tests were introduced for linear models by Michalski and Zmyślony (1996, 1999). When the observations are taken in not perfectly standardized conditions the F tests have generalized F distributions with random non-centrality parameters, see Nunes and Mexia (2006). We now study the case of nearly normal perturbations leading to Gamma distributed non-centrality parameters.

How to cite

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Célia Maria Pinto Nunes, Sandra Maria Bargão Saraiva Ferreira, and Dário Jorge da Conceição Ferreira. "Generalized F tests in models with random perturbations: the gamma case." Discussiones Mathematicae Probability and Statistics 29.2 (2009): 185-197. <http://eudml.org/doc/277035>.

@article{CéliaMariaPintoNunes2009,
abstract = {Generalized F tests were introduced for linear models by Michalski and Zmyślony (1996, 1999). When the observations are taken in not perfectly standardized conditions the F tests have generalized F distributions with random non-centrality parameters, see Nunes and Mexia (2006). We now study the case of nearly normal perturbations leading to Gamma distributed non-centrality parameters.},
author = {Célia Maria Pinto Nunes, Sandra Maria Bargão Saraiva Ferreira, Dário Jorge da Conceição Ferreira},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {generalized F distributions; random non-centrality parameters; Gamma distribution; generalized distributions; gamma distribution},
language = {eng},
number = {2},
pages = {185-197},
title = {Generalized F tests in models with random perturbations: the gamma case},
url = {http://eudml.org/doc/277035},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Célia Maria Pinto Nunes
AU - Sandra Maria Bargão Saraiva Ferreira
AU - Dário Jorge da Conceição Ferreira
TI - Generalized F tests in models with random perturbations: the gamma case
JO - Discussiones Mathematicae Probability and Statistics
PY - 2009
VL - 29
IS - 2
SP - 185
EP - 197
AB - Generalized F tests were introduced for linear models by Michalski and Zmyślony (1996, 1999). When the observations are taken in not perfectly standardized conditions the F tests have generalized F distributions with random non-centrality parameters, see Nunes and Mexia (2006). We now study the case of nearly normal perturbations leading to Gamma distributed non-centrality parameters.
LA - eng
KW - generalized F distributions; random non-centrality parameters; Gamma distribution; generalized distributions; gamma distribution
UR - http://eudml.org/doc/277035
ER -

References

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  1. [1] R.B. Davies, Algorithm AS 155: The distribution of a linear combinations of χ² random variables, Applied Statistics 29 (1980), 232-333. Zbl0473.62025
  2. [2] J.P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika 48 (1961), 419-426. Zbl0136.41103
  3. [3] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discuss. Math. Probab. Stat. 22 (2002), 37-51. Zbl1037.62004
  4. [4] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimators and Tests for Variance Components in Cross Nested Orthogonal Designs, Discuss. Math. Probab. Stat. 23 (2) (2003a), 175-201. Zbl1049.62065
  5. [5] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimating and testing of variance components: an application to a grapevine experiment, Biometrical Letters 40 (1) (2003b), 1-7. 
  6. [6] D.W. Gaylor and F.N. Hopper, Estimating the degrees of freedom for linear combinations of mean squares by Satterthwaite's formula, Technometrics 11 (1969), 691-706. 
  7. [7] A.I. Khuri, T. Mathew and B.K. Sinha, Statistical Tests for Mixed Linear Models, A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York 1998. Zbl0893.62009
  8. [8] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310. Zbl0842.62059
  9. [9] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 17 (1999), 103-110. Zbl0987.62012
  10. [10] C. Nunes and J.T. Mexia, Non-central generalized F distributions, Discuss. Math. Probab. Stat. 26 (1) (2006), 47-61. Zbl1128.62018
  11. [11] C. Nunes, I. Pinto and J.T. Mexia, F and Selective F tests with balanced cross-nesting and associated models, Discuss. Math. Probab. Stat. 26 (2) (2006), 193-205. Zbl1128.62080
  12. [12] H. Robbins, Mixture of distribution, Ann. Math. Statistics 19 (1948), 360-369. Zbl0037.36301
  13. [13] H. Robbins and E.J.G. Pitman, Application of the method of mixtures to quadratic forms in normal variates, Ann. Math. Statistics 20 (1949), 552-560. Zbl0036.20801
  14. [14] F.E. Satterthwaite, An approximate distribution of estimates of variance components, Biometrics Bulletin 2 (1946), 110-114. 

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