Outliers and influence under arbitrary variance

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dc.contributor.advisorDunne, Timothy Terenceen_ZA
dc.contributor.authorSchall, Roberten_ZA
dc.date.accessioned2016-09-25T16:47:56Z
dc.date.available2016-09-25T16:47:56Z
dc.date.issued1986en_ZA
dc.description.abstractUsing a geometric approach to best linear unbiased estimation in the general linear model, the additional sum of squares principle, used to generate decompositions, can be generalized allowing for an efficient treatment of augmented linear models. The notion of the admissibility of a new variable is useful in augmenting models. Best linear unbiased estimation and tests of hypotheses can be performed through transformations and reparametrizations of the general linear model. The theory of outliers and influential observations can be generalized so as to be applicable for the general univariate linear model, where three types of outlier and influence may be distinguished. The adjusted models, adjusted parameter estimates, and test statistics corresponding to each type of outlier are obtained, and data adjustments can be effected. Relationships to missing data problems are exhibited. A unified approach to outliers in the general linear model is developed. The concept of recursive residuals admits generalization. The typification of outliers and influential observations in the general linear model can be extended to normal multivariate models. When the outliers in a multivariate regression model follow a nested pattern, maximum likelihood estimation of the parameters in the model adjusted for the different types of outlier can be performed in closed form, and the corresponding likelihood ratio test statistic is obtained in closed form. For an arbitrary outlier pattern, and for the problem of outliers in the generalized multivariate regression model, three versions of the EM-algorithm corresponding to three types of outlier are used to obtain maximum likelihood estimates iteratively. A fundamental principle is the comparison of observations with a choice of distribution appropriate to the presumed type of outlier present. Applications are not necessarily restricted to multivariate normality.en_ZA
dc.identifier.apacitationSchall, R. (1986). <i>Outliers and influence under arbitrary variance</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Statistical Sciences. Retrieved from http://hdl.handle.net/11427/21913en_ZA
dc.identifier.chicagocitationSchall, Robert. <i>"Outliers and influence under arbitrary variance."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 1986. http://hdl.handle.net/11427/21913en_ZA
dc.identifier.citationSchall, R. 1986. Outliers and influence under arbitrary variance. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Schall, Robert AB - Using a geometric approach to best linear unbiased estimation in the general linear model, the additional sum of squares principle, used to generate decompositions, can be generalized allowing for an efficient treatment of augmented linear models. The notion of the admissibility of a new variable is useful in augmenting models. Best linear unbiased estimation and tests of hypotheses can be performed through transformations and reparametrizations of the general linear model. The theory of outliers and influential observations can be generalized so as to be applicable for the general univariate linear model, where three types of outlier and influence may be distinguished. The adjusted models, adjusted parameter estimates, and test statistics corresponding to each type of outlier are obtained, and data adjustments can be effected. Relationships to missing data problems are exhibited. A unified approach to outliers in the general linear model is developed. The concept of recursive residuals admits generalization. The typification of outliers and influential observations in the general linear model can be extended to normal multivariate models. When the outliers in a multivariate regression model follow a nested pattern, maximum likelihood estimation of the parameters in the model adjusted for the different types of outlier can be performed in closed form, and the corresponding likelihood ratio test statistic is obtained in closed form. For an arbitrary outlier pattern, and for the problem of outliers in the generalized multivariate regression model, three versions of the EM-algorithm corresponding to three types of outlier are used to obtain maximum likelihood estimates iteratively. A fundamental principle is the comparison of observations with a choice of distribution appropriate to the presumed type of outlier present. Applications are not necessarily restricted to multivariate normality. DA - 1986 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1986 T1 - Outliers and influence under arbitrary variance TI - Outliers and influence under arbitrary variance UR - http://hdl.handle.net/11427/21913 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/21913
dc.identifier.vancouvercitationSchall R. Outliers and influence under arbitrary variance. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 1986 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/21913en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Statistical Sciencesen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Statisticsen_ZA
dc.titleOutliers and influence under arbitrary varianceen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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