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On estimation in multilevel models with block circular symmetric covariance structure
Stockholm University, Faculty of Social Sciences, Department of Statistics.
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2012 (English)In: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 16, no 1, p. 83-96Article in journal (Refereed) Published
Abstract [en]

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

Place, publisher, year, edition, pages
2012. Vol. 16, no 1, p. 83-96
Keywords [en]
Circular block symmetry, constrained model, patterned covariance matrix, explicit maximum likelihood estimator, multilevel model
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-84275OAI: oai:DiVA.org:su-84275DiVA, id: diva2:579413
Available from: 2012-12-20 Created: 2012-12-20 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Contributions to Estimation and Testing Block Covariance Structures in Multivariate Normal Models
Open this publication in new window or tab >>Contributions to Estimation and Testing Block Covariance Structures in Multivariate Normal Models
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns inference problems in balanced random effects models with a so-called block circular Toeplitz covariance structure. This class of covariance structures describes the dependency of some specific multivariate two-level data when both compound symmetry and circular symmetry appear simultaneously.

We derive two covariance structures under two different invariance restrictions. The obtained covariance structures reflect both circularity and exchangeability present in the data. In particular, estimation in the balanced random effects with block circular covariance matrices is considered. The spectral properties of such patterned covariance matrices are provided. Maximum likelihood estimation is performed through the spectral decomposition of the patterned covariance matrices. Existence of the explicit maximum likelihood estimators is discussed and sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and the corresponding maximum likelihood estimators are presented.

This thesis also deals with hypothesis testing of block covariance structures, especially block circular Toeplitz covariance matrices. We consider both so-called external tests and internal tests. In the external tests, various hypotheses about testing block covariance structures, as well as mean structures, are considered, and the internal tests are concerned with testing specific covariance parameters given the block circular Toeplitz structure. Likelihood ratio tests are constructed, and the null distributions of the corresponding test statistics are derived.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm Univeristy, 2015. p. 54
Keywords
Block circular symmetry, covariance parameters, explicit maximum likelihood estimator, likelihood ratio test, restricted model, Toeplitz matrix
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-115347 (URN)978-91-7649-136-2 (ISBN)
Public defence
2015-05-11, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2015-04-17 Created: 2015-03-19 Last updated: 2015-04-20Bibliographically approved

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