Abstract
This work aims to introduce a new method of estimating the variance components in mixed linear models . The approach will be done firstly for models with 3 variances components and secondly attention will be devoted to general case of models with an arbitrary number of variance components . In our approach, we construct and apply a finite sequence of orthogonal matrices to the mixed linear model variance-covariance structure in order to produce a set of Gauss–Markov sub-models which will be used to create pooled estimators for the variance components . Numerical results will be given, comparing the performance of our proposed estimator to the one based on likelihood procedure.
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Acknowledgements
This work was partially supported by the Fundaç ao para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through PEst-OE/MAT/UI0297/2011 (CMA), and by the Fundaç ao Calouste Gulbenkian Through a PhD Grants. It was also partially supported by Universidade de Cabo Verde.
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Silva, A., Fonseca, M., Mexia, J. (2017). Variance Components Estimation in Mixed Linear Model—The Sub-diagonalization Method. In: Bebiano, N. (eds) Applied and Computational Matrix Analysis. MAT-TRIAD 2015. Springer Proceedings in Mathematics & Statistics, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-49984-0_21
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DOI: https://doi.org/10.1007/978-3-319-49984-0_21
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