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dc.contributor.authorYavarizadeh, Bahareh
dc.date.accessioned2021-05-13T20:09:52Z
dc.date.available2021-05-13T20:09:52Z
dc.identifier.urihttp://hdl.handle.net/10464/15079
dc.description.abstractLinear mixed models (LMMs) are an important tool for the analysis of a broad range of structures including longitudinal data, repeated measures data (including cross-over studies), growth and dose-response curve data, clustered (or nested) data, multivariate data, and correlated data. In many practical situations, the observation of variables is subject to measurement errors, and ignoring these in data analysis can lead to inconsistent parameter estimation and invalid statistical inference. Therefore, it is necessary to extend LMMs by taking the effect of measurement errors into account. Multicollinearity and fixed-effect variables with measurement errors are two well-known problems in the analysis of linear regression models. Although there exists a large amount of research on these two problems, there is by now no single technique superior to all other techniques for the analysis of regression models when these problems are present. In this thesis, we propose two new estimators using Nakamura's approach in LMM with measurement errors to overcome multicollinearity. We consider that prior information is available on fixed and random effects. The first estimator is the new mixed ridge estimator (NMRE) and the second estimator is the weighted mixed ridge estimator (WMRE). We investigate the asymptotic properties of these proposed estimators and compare the performance of them over the other estimators using the mean square error matrix (MSEM) criterion. Finally, a data example and a Monte Carlo simulation are also provided to show the theoretical results.en_US
dc.language.isoengen_US
dc.publisherBrock Universityen_US
dc.subjectLinear Mixed Modelsen_US
dc.subjectMulticollinearityen_US
dc.subjectNew Mixed Ridge Estimatoren_US
dc.subjectWeighted Mixed Ridge Estimatoren_US
dc.subjectMeasurement erroren_US
dc.titleSome New Estimator in Linear Mixed Models with Measurement erroren_US
dc.typeElectronic Thesis or Dissertationen_US
dc.degree.nameM.Sc. Mathematics and Statisticsen_US
dc.degree.levelMastersen_US
dc.contributor.departmentDepartment of Mathematicsen_US
dc.degree.disciplineFaculty of Mathematics and Scienceen_US
refterms.dateFOA2021-08-18T01:34:42Z


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