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2009 | 29 | 2 | 185-197
Tytuł artykułu

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

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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.
Twórcy
  • Department of Mathematics, University of Beira Interior 6200 Covilhã, Portugal
  • Department of Mathematics, University of Beira, Interior 6200 Covilhã, Portugal
  • Department of Mathematics, University of Beira, Interior 6200 Covilhã, Portugal
Bibliografia
  • [1] R.B. Davies, Algorithm AS 155: The distribution of a linear combinations of χ² random variables, Applied Statistics 29 (1980), 232-333.
  • [2] J.P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika 48 (1961), 419-426.
  • [3] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discuss. Math. Probab. Stat. 22 (2002), 37-51.
  • [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.
  • [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] 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] 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.
  • [8] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.
  • [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.
  • [10] C. Nunes and J.T. Mexia, Non-central generalized F distributions, Discuss. Math. Probab. Stat. 26 (1) (2006), 47-61.
  • [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.
  • [12] H. Robbins, Mixture of distribution, Ann. Math. Statistics 19 (1948), 360-369.
  • [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.
  • [14] F.E. Satterthwaite, An approximate distribution of estimates of variance components, Biometrics Bulletin 2 (1946), 110-114.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1114
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