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Contributions to Estimation and Testing Block Covariance Structures in Multivariate Normal Models
Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
2015 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: Department of Statistics, Stockholm Univeristy , 2015. , s. 54
Nyckelord [en]
Block circular symmetry, covariance parameters, explicit maximum likelihood estimator, likelihood ratio test, restricted model, Toeplitz matrix
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
statistik
Identifikatorer
URN: urn:nbn:se:su:diva-115347ISBN: 978-91-7649-136-2 (tryckt)OAI: oai:DiVA.org:su-115347DiVA, id: diva2:796644
Disputation
2015-05-11, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (Engelska)
Opponent
Handledare
Tillgänglig från: 2015-04-17 Skapad: 2015-03-19 Senast uppdaterad: 2020-01-16Bibliografiskt granskad
Delarbeten
1. Block Circular Symmetry in Multilevel Models
Öppna denna publikation i ny flik eller fönster >>Block Circular Symmetry in Multilevel Models
2011 (Engelska)Rapport (Övrigt vetenskapligt)
Abstract [en]

Models that describe symmetries present in the error structure of observations have been widely used in dierent applications, with early examples from psychometric and medical research. The aim of this article is to study a multilevel model with a covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.

Ort, förlag, år, upplaga, sidor
Stockholm: Department of Statistics, Stockholm University, 2011. s. 23
Serie
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 3
Nyckelord
Covariance matrix, Circular block symmetry, Multilevel model, Symmetry model, Spectrum
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
statistik
Identifikatorer
urn:nbn:se:su:diva-72075 (URN)
Tillgänglig från: 2012-09-10 Skapad: 2012-02-02 Senast uppdaterad: 2019-12-17Bibliografiskt granskad
2. On estimation in multilevel models with block circular symmetric covariance structure
Öppna denna publikation i ny flik eller fönster >>On estimation in multilevel models with block circular symmetric covariance structure
2012 (Engelska)Ingår i: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 16, nr 1, s. 83-96Artikel i tidskrift (Refereegranskat) 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.

Nyckelord
Circular block symmetry, constrained model, patterned covariance matrix, explicit maximum likelihood estimator, multilevel model
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
statistik
Identifikatorer
urn:nbn:se:su:diva-84275 (URN)
Tillgänglig från: 2012-12-20 Skapad: 2012-12-20 Senast uppdaterad: 2019-12-17Bibliografiskt granskad
3. On estimation in hierarchical models with block circular covariance structures
Öppna denna publikation i ny flik eller fönster >>On estimation in hierarchical models with block circular covariance structures
2015 (Engelska)Ingår i: Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, E-ISSN 1572-9052, Vol. 67, nr 4, s. 773-791Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Hierarchical linear models with a block circular covariance structure are considered. Sufficient conditions for obtaining explicit and unique estimators for the variance–covariance components are derived. Different restricted models are discussed and maximum likelihood estimators are presented. The theory is illustrated through covariance matrices of small sizes and a real-life example.

Nyckelord
Circular block symmetry, Estimation, Identifiability, Maximum likelihood estimator, Restricted model, Variance components
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
statistik
Identifikatorer
urn:nbn:se:su:diva-107708 (URN)10.1007/s10463-014-0475-8 (DOI)000356541300007 ()
Tillgänglig från: 2014-09-24 Skapad: 2014-09-24 Senast uppdaterad: 2019-12-17Bibliografiskt granskad
4. Testing in multivariate normal models with block circular covariance structures
Öppna denna publikation i ny flik eller fönster >>Testing in multivariate normal models with block circular covariance structures
2015 (Engelska)Rapport (Övrigt vetenskapligt)
Abstract [en]

In this article, the results concerning hypothesis testing in multivariate normal models with block circular covariance structures are obtained. Hypotheses about a general block structure of the covariance matrix and specific covariance parameters have been of main interest. In addition, the tests about patterned mean vectors have been considered.The corresponding likelihood ratio statistics are derived and their null distributions are studied.

Ort, förlag, år, upplaga, sidor
Stockholm: Department of Statistics, Stockholm University, 2015
Serie
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 2
Nyckelord
Beta random variables, Canonical reduction, Covariance parameters, Likelihood ratio test, Restricted model
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
statistik
Identifikatorer
urn:nbn:se:su:diva-115320 (URN)
Tillgänglig från: 2015-03-25 Skapad: 2015-03-19 Senast uppdaterad: 2019-12-17Bibliografiskt granskad

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