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Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models
Discussiones Mathematicae. Probability and Statistics, Tome 29 (2009) no. 1, pp. 5-29

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The paper deals with construction of exact confidence intervals for the variance component σ₁² and ratio θ of variance components σ₁² and σ² in mixed linear models for the family of normal distributions _t(0, σ₁²W + σ²I_t). This problem essentially depends on algebraic structure of the covariance matrix W (see Gnot and Michalski, 1994, Michalski and Zmyślony, 1996). In the paper we give two classes of bayesian interval estimators depending on a prior distribution on (σ₁², σ²) for:
Keywords: mixed linear models, variance components, hypothesis testing, confidence intervals, generalized p-values 
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Michalski, Andrzej. Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models. Discussiones Mathematicae. Probability and Statistics, Tome 29 (2009) no. 1, pp. 5-29. http://geodesic.mathdoc.fr/item/DMPS_2009_29_1_a0/