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Article: Estimation and robustness of linear mixed models in credibility context

TitleEstimation and robustness of linear mixed models in credibility context
Authors
KeywordsLinear mixed model
Hachemeister’s model
Dannenburg’s crossed classification model
Maximum likelihood estimator
Restricted maximum likelihood estimator
Issue Date2010
PublisherCasualty Actuarial Society. The Journal's web site is located at http://www.variancejournal.org
Citation
Variance: advancing the science of risk, 2010, v. 4 n. 1, p. 66-80 How to Cite?
AbstractIn this paper, linear mixed models are employed for estimation of structural parameters in credibility context. In particular, Hachemeister’s model and Dannenburg’s crossed classification model are considered. Maximum likelihood (ML) and restricted maximum likelihood (REML) methods are developed to estimate the variance and covariance parameters. These estimators are compared with the classical Hachemeister’s and the Dannenburg’s estimators by simulation. The robustness properties of the ML and REML methods are also investigated. In the simulation studies, we have tested the performance of ML, REML, and the classical estimation approaches when the error terms are normally distributed and lognormally distributed. It is noticed that the proposed ML and REML approaches have clear advantages over the classical estimation approaches. The mean-squared errors of the proposed estimators can be a few hundred times smaller than those of classical estimators.
Persistent Identifierhttp://hdl.handle.net/10722/137544
ISSN

 

DC FieldValueLanguage
dc.contributor.authorFung, TWKen_US
dc.contributor.authorXu, XCen_US
dc.date.accessioned2011-08-26T14:27:40Z-
dc.date.available2011-08-26T14:27:40Z-
dc.date.issued2010en_US
dc.identifier.citationVariance: advancing the science of risk, 2010, v. 4 n. 1, p. 66-80en_US
dc.identifier.issn1940-6444-
dc.identifier.urihttp://hdl.handle.net/10722/137544-
dc.description.abstractIn this paper, linear mixed models are employed for estimation of structural parameters in credibility context. In particular, Hachemeister’s model and Dannenburg’s crossed classification model are considered. Maximum likelihood (ML) and restricted maximum likelihood (REML) methods are developed to estimate the variance and covariance parameters. These estimators are compared with the classical Hachemeister’s and the Dannenburg’s estimators by simulation. The robustness properties of the ML and REML methods are also investigated. In the simulation studies, we have tested the performance of ML, REML, and the classical estimation approaches when the error terms are normally distributed and lognormally distributed. It is noticed that the proposed ML and REML approaches have clear advantages over the classical estimation approaches. The mean-squared errors of the proposed estimators can be a few hundred times smaller than those of classical estimators.-
dc.languageengen_US
dc.publisherCasualty Actuarial Society. The Journal's web site is located at http://www.variancejournal.orgen_US
dc.relation.ispartofVariance: advancing the science of risken_US
dc.subjectLinear mixed model-
dc.subjectHachemeister’s model-
dc.subjectDannenburg’s crossed classification model-
dc.subjectMaximum likelihood estimator-
dc.subjectRestricted maximum likelihood estimator-
dc.titleEstimation and robustness of linear mixed models in credibility contexten_US
dc.typeArticleen_US
dc.identifier.emailFung, TWK: wingfung@hku.hken_US
dc.identifier.authorityFung, TWK=rp00696en_US
dc.description.naturelink_to_OA_fulltext-
dc.identifier.hkuros189442en_US
dc.identifier.volume4en_US
dc.identifier.issue1en_US
dc.identifier.spage66en_US
dc.identifier.epage80en_US

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