Variance components estimation in mixed linear model—the sub-diagonalization method

A. Silva; M. Fonseca; J. Mexia

doi:10.1007/978-3-319-49984-0_21

Variance components estimation in mixed linear model—the sub-diagonalization method

A. Silva, M. Fonseca, J. Mexia

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

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.

Original language	English
Title of host publication	Applied and Computational Matrix Analysis - MAT-TRIAD, Selected, Revised Contributions
Publisher	Springer New York LLC
Pages	317-341
Number of pages	25
Volume	192
ISBN (Print)	9783319499826
DOIs	https://doi.org/10.1007/978-3-319-49984-0_21
Publication status	Published - 1 Jan 2017
Event	International Conference on Matrix Analysis and its Applications, MAT-TRIAD 2015 - Coimbra, Portugal Duration: 7 Sept 2015 → 11 Sept 2015

Conference

Conference	International Conference on Matrix Analysis and its Applications, MAT-TRIAD 2015
Country/Territory	Portugal
City	Coimbra
Period	7/09/15 → 11/09/15

Keywords

Mixed linear model
Orthogonal matrices
Simultaneous diagonalization
Variance components

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Cite this

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title = "Variance components estimation in mixed linear model—the sub-diagonalization method",

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.",

keywords = "Mixed linear model, Orthogonal matrices, Simultaneous diagonalization, Variance components",

author = "A. Silva and M. Fonseca and J. Mexia",

note = "Sem PDF.; International Conference on Matrix Analysis and its Applications, MAT-TRIAD 2015 ; Conference date: 07-09-2015 Through 11-09-2015",

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doi = "10.1007/978-3-319-49984-0_21",

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Silva, A, Fonseca, M & Mexia, J 2017, Variance components estimation in mixed linear model—the sub-diagonalization method. in Applied and Computational Matrix Analysis - MAT-TRIAD, Selected, Revised Contributions. vol. 192, Springer New York LLC, pp. 317-341, International Conference on Matrix Analysis and its Applications, MAT-TRIAD 2015, Coimbra, Portugal, 7/09/15. https://doi.org/10.1007/978-3-319-49984-0_21

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AU - Silva, A.

AU - Fonseca, M.

AU - Mexia, J.

N1 - Sem PDF.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Mixed linear model

KW - Orthogonal matrices

KW - Simultaneous diagonalization

KW - Variance components

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DO - 10.1007/978-3-319-49984-0_21

M3 - Conference contribution

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SN - 9783319499826

VL - 192

SP - 317

EP - 341

BT - Applied and Computational Matrix Analysis - MAT-TRIAD, Selected, Revised Contributions

PB - Springer New York LLC

T2 - International Conference on Matrix Analysis and its Applications, MAT-TRIAD 2015

Y2 - 7 September 2015 through 11 September 2015

ER -

Variance components estimation in mixed linear model—the sub-diagonalization method

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Keywords

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